{
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 泊松分布（Poisson Distribution）\n",
    "***\n",
    "## 定义：\n",
    "\n",
    "现实生活多数服从于泊松分布\n",
    "\n",
    "假设你在一个呼叫中心工作，一天里你大概会接到多少个电话？它可以是任何一个数字。现在，呼叫中心一天的呼叫总数可以用泊松分布来建模。这里有一些例子：\n",
    "\n",
    "- 医院在一天内录制的紧急电话的数量。\n",
    "- 某个地区在一天内报告的失窃的数量。\n",
    "- 在一小时内抵达沙龙的客户人数。\n",
    "- 在特定城市上报的自杀人数。\n",
    "- 书中每一页打印错误的数量。\n",
    "泊松分布适用于在随机时间和空间上发生事件的情况，其中，我们只关注事件发生的次数。\n",
    "\n",
    "当以下假设有效时，则称为泊松分布\n",
    "\n",
    "- 任何一个成功的事件都不应该影响另一个成功的事件。\n",
    "- 在短时间内成功的概率必须等于在更长的间内成功的概率。\n",
    "- 时间间隔很小时，在给间隔时间内成功的概率趋向于零。\n",
    "\n",
    "泊松分布中使用了这些符号：\n",
    "\n",
    "- λ是事件发生的速率\n",
    "- t是时间间隔的长\n",
    "- X是该时间间隔内的事件数。\n",
    "- 其中，X称为泊松随机变量，X的概率分布称为泊松分布。\n",
    "\n",
    "- 令μ表示长度为t的间隔中的平均事件数。那么，µ = λ*t。\n",
    "\n",
    "\n",
    "例如说一个医院中，每个病人来看病都是随机并独立的概率，则该医院一天（或者其他特定时间段，一小时，一周等等）接纳的病人总数可以看做是一个服从poisson分布的随机变量。但是为什么可以这样处理呢？\n",
    "通俗定义：假定一个事件在一段时间内随机发生，且符合以下条件：\n",
    "- （1）将该时间段无限分隔成若干个小的时间段，在这个接近于零的小时间段里，该事件发生一次的概率与这个极小时间段的长度成正比。\n",
    "- （2）在每一个极小时间段内，该事件发生两次及以上的概率恒等于零。\n",
    "- （3）该事件在不同的小时间段里，发生与否相互独立。\n",
    "\n",
    "则该事件称为poisson process。这个第二定义就更加利于大家理解了，回到医院的例子之中，如果我们把一天分成24个小时，或者24x60分钟，或者24x3600秒。时间分的越短，这个时间段里来病人的概率就越小（比如说医院在正午12点到正午12点又一毫秒之间来病人的概率是不是很接近于零？）。 条件一符合。另外如果我们把时间分的很细很细，是不是同时来两个病人（或者两个以上的病人）就是不可能的事件？即使两个病人同时来，也总有一个人先迈步子跨进医院大门吧。条件二也符合。倒是条件三的要求比较苛刻。应用到实际例子中就是说病人们来医院的概率必须是相互独立的，如果不是，则不能看作是poisson分布。\n",
    "\n",
    "## 公式\n",
    "\n",
    "###  $$ f(x|\\lambda) = \\frac{\\lambda^{x}e^{-\\lambda}}{x!}$$\n",
    "### where $\\lambda$ denotes the mean of the distribution.\n",
    "\n",
    "已知平均每小时出生3个婴儿，请问下一个小时，会出生几个？\n",
    "\n",
    "有可能一下子出生6个，也有可能一个都不出生。这是我们没法知道的。\n",
    "\n",
    "泊松分布就是描述某段时间内，事件具体的发生概率。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ### 该公式是泊松分布的公式。等号的左边，P 表示概率，N表示某种函数关系，t 表示时间，n 表示数量，1小时内出生3个婴儿的概率，就表示为 P(N(1) = 3) 。等号的右边，λ 表示事件的频率。\n",
    "<img src=\"2.png\" style=\"width:200px;height:100px;float:left\"> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 接下来两个小时，一个婴儿都不出生的概率是0.25%，基本不可能发生。\n",
    "<img src=\"3.png\" style=\"width:250px;height:100px;float:left\">    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 接下来一个小时，至少出生两个婴儿的概率是80%。\n",
    "<img src=\"4.png\" style=\"width:350px;height:230px;float:left\">"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
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dRZIkSVIrpPWOYoxxfgjhFuCqEMIjpLazGAVcDTwH3N9g+DRgBKl9F3f7WQhhCPBnUnsnFgLHABcAW4Fv7nHLbwOnAk+HEG4EtpAqpcOASTFG91zoBMaWvr+gzXEH9m1htCRJkqRMke5iNpB6mvg2cAUwCVgP/BT4ToyxroVzfwN8Efg8qVVOI6nCeDvw3zHGpQ0HxxjfCiF8BPhP4FtAATAbODPGOLUVmZWg/j27UdqnO3Nc+VSSJEnqVNIuijHGWmBK/Vdz4w5o4tiDwIOtCRZjXAh8ojXnKPNUlJXw6lKLoiRJktSZpPuOorRPKspKWLFpJ+u27m0bTkmSJEmZxqKodlVe9v57ipIkSZI6B4ui2tWYocXk5gTmLrcoSpIkSZ2FRVHtqntBLocN6uWCNpIkSVInYlFUu6sYXsLcZZuoq3NXE0mSJKkzsCiq3VWUlrClsoYlG7YnHUWSJElSGiyKancuaCNJkiR1LhZFtbuDB/akqCDXoihJkiR1EhZFtbvcnMCRpcUuaCNJkiR1EhZFdYiKsj68vmoLu2pqk44iSZIkqQUWRXWIirJiqmsjr6/cknQUSZIkSS2wKKpDuKCNJEmS1HlYFNUhhhR3Z1DvbsxdvjnpKJIkSZJaYFFUhykvLXFBG0mSJKkTsCiqw1QML2HJ+u1s2lGVdBRJkiRJzbAoqsNUlKbeU5zn9FNJkiQpo1kU1WGOLC0mBJx+KkmSJGU4i6I6TK/CfA4e0NOVTyVJkqQMZ1FUhyovSy1oE2NMOookSZKkvbAoqkNVlJWwYXsVy9/dmXQUSZIkSXthUVSHqihLLWgzd7nTTyVJkqRMZVFUhzpscC+65eUwZ6lFUZIkScpUFkV1qPzcHMYMK/aJoiRJkpTBLIrqcOWlJcxfsZnq2rqko0iSJElqgkVRHa5ieAmV1XX8bc3WpKNIkiRJaoJFUR2uorR+QZtlmxNOIkmSJKkpFkV1uLK+3elbVMCcZe8mHUWSJElSEyyK6nAhBMpLi32iKEmSJGUoi6ISUV5Wwt/WbmXbrpqko0iSJEnag0VRiSgvKyFGmL/cp4qSJElSprEoKhHvLWjjfoqSJElSxrEoKhF9igoY0a8Hc5ZaFCVJkqRMY1FUYirKSnyiKEmSJGUgi6ISU15awqrNlazZUpl0FEmSJEkNWBSVmPKy1HuKc5b5VFGSJEnKJBZFJWb00N7k5QTmWhQlSZKkjJJWUQwh5IQQrg0hvBFCqAwhLAshTAkhFKVx7qEhhO+FEF4KIawLIWwNIcwJIfxrU+eHEK4PIcS9fP3jvvyQykyF+bmMGtLbJ4qSJElShslLc9yNwNXAo8AUYFT9r48KIUyMMdY1c+4lwFeBPwD3AdXAycB/AOeHEI6PMe5s4rxrgfV7HJuVZl51EhVlJTz66grq6iI5OSHpOJIkSZJIoyiGEEYDXwMeiTGe1+D4EuAnwAXA/c1c4iHghzHGhjur3xZCeBP4V+BS4OYmznssxvh2iz+BOrXyshJ+/dI7LF6/jYMH9ko6jiRJkiTSm3p6IRCAm/Y4fiewA7iouZNjjDP3KIm7PVD/fczezg0h9A4hpPvUU51QRVkxAK+6n6IkSZKUMdIpiscCdcDLDQ/GGCuBOfWf74vS+u9r9vL5PGAzUBlCmBFC+Ng+3kcZbGT/nvTqlud+ipIkSVIGSacoDgXWxxh3NfHZCqB/CKGgNTcNIeQC3wFq+OC01U3AHaSmu34C+DYwAngihHBxa+6jzJeTExhbVuyCNpIkSVIGSWdaZw+gqZIIUNlgTFUr7nsTcDzwLzHGRQ0/iDHuOcWVEMJdwALgxhDCQzHGbU1dNIRwBXAFwPDhw1sRR0mqKCvh9ucWU1ldS2F+btJxJEmSpC4vnSeKO4Bue/mssMGYtIQQvg9cBdwRY/xhOufEGDcAtwElwPhmxt0RYxwXYxw3YMCAdCMpYeWlJdTURV5buSXpKJIkSZJIryiuJDW9tKmyOIzUtNS0niaGEK4H/g24G/iHdEPWe7v+e/9WnqcMV1FWAuD0U0mSJClDpFMUX6kfd1zDgyGEQqACmJnOjUII1wHXAfcAl8UYY+uickj9970tfqNOamDvQoYWFzLXoihJkiRlhHSK4gNABK7Z4/jlpN5NvG/3gRDCQSGEw/e8QAjhO8D1wK+BL8UY65q6UQghL4RQ3MTxMuBKYAMwI43M6mTKy0p8oihJkiRliBYXs4kxzg8h3AJcFUJ4BPhfYBRwNfAcjVctnUZqhdKw+0AI4avAd4GlwFTgsyGEBqewJsb4TP0/9wSWhBAeAxYC7wKHAZfVf3ZhjHHnPvycynAVZSX8acFqNm6vom9RqxbRlSRJktTG0t3M/hpS7wheAUwC1gM/Bb6zt6eDDezeZ3E48KsmPn8O2F0UdwIPAx8CJpMqh+tJFcwfxRhfbuJ8ZYHy+vcU5y7fxMmHDUw4jSRJktS1pVUUY4y1wJT6r+bGHdDEsYuBi9O8zy5STw/VxRw5rJicAHOWWhQlSZKkpKXzjqLU7oq65XHooF7MXe57ipIkSVLSLIrKGOWlJcxdtonWL4grSZIkqS1ZFJUxystKeHdHNUs37kg6iiRJktSlWRSVMSrqF7RxmwxJkiQpWRZFZYxDB/Wke36uRVGSJElKmEVRGSMvN4cjhxUz16IoSZIkJcqiqIxSXlbMgpVbqK5taXtOSZIkSe3FoqiMUl5WQlVNHW+s2pp0FEmSJKnLsigqo7y3oI37KUqSJEmJsSgqowwr6U7/ngXMWWpRlCRJkpJiUVRGCSFQUVbCXJ8oSpIkSYmxKCrjlJeW8Pd129hSWZ10FEmSJKlLsigq45SXlRAjzF++OekokiRJUpdkUVTGKS+tX9DG/RQlSZKkRFgUlXGKe+Qzsn+RRVGSJElKiEVRGamirIQ5yzYRY0w6iiRJktTlWBSVkcrLSli3dRert1QmHUWSJEnqciyKykjlZfXvKbqfoiRJktThLIrKSKOG9KIgN4c57qcoSZIkdTiLojJSt7xcRg3t7RNFSZIkKQEWRWWso8pKmL9iM7V1LmgjSZIkdSSLojJWeVkxO6pqeWvttqSjSJIkSV2KRVEZq7y0fkGbZe8mnESSJEnqWiyKylgH9i+id2Eec5ZtTjqKJEmS1KVYFJWxQgiUl5Uwd5kL2kiSJEkdyaKojHZUWQmL1mxlZ1Vt0lEkSZKkLsOiqIxWXlZCbV1kwUqnn0qSJEkdxaKojFZeVr+gjfspSpIkSR3GoqiM1r9nN0r7dGfOcouiJEmS1FEsisp4LmgjSZIkdSyLojJeRWkJy9/dyfptu5KOIkmSJHUJFkVlvIrhqfcUfaooSZIkdQyLojLemKHF5OYE5lgUJUmSpA5hUVTG616Qy2GDelkUJUmSpA5iUVSnsHtBmxhj0lEkSZKkrGdRVKdQUVbMlsoalqzfnnQUSZIkKetZFNUpVJT1AWCu+ylKkiRJ7S7tohhCyAkhXBtCeCOEUBlCWBZCmBJCKErj3ENDCN8LIbwUQlgXQtgaQpgTQvjXvZ0fQjgshPBYCOHdEML2EML0EMIprfnhlD0OHtiTooJc5iy1KEqSJEntrTVPFG8EbgBeB74G/A64Gng8hNDSdS4BrgX+DnwP+CdgEfAfwIwQQveGg0MIBwEzgA8DP6of3xN4KoQwsRWZlSVycwJHlhYzZ/nmpKNIkiRJWS8vnUEhhNGkyuEjMcbzGhxfAvwEuAC4v5lLPAT8MMbY8E/5t4UQ3gT+FbgUuLnBZz8ESoBjYoxz6u91D/AacEsI4fDoqiZdTnlZCXf/9W121dTSLS836TiSJElS1kr3ieKFQABu2uP4ncAO4KLmTo4xztyjJO72QP33MbsP1E9FPQd4dndJrL/GNuDnwKHAsWnmVhapKC2hqraOhau2Jh1FkiRJymrpFsVjgTrg5YYHY4yVwBz2vbiV1n9f0+DYWKAb8GIT419qkEddTMXwEgDmup+iJEmS1K7SLYpDgfUxxl1NfLYC6B9CKGjNjUMIucB3gBoaT1sd2uC6Td0LYNhernlFCGFmCGHmunXrWhNHncDg3oUM7NWNORZFSZIkqV2lWxR7AE2VRIDKBmNa4ybgeOA7McZFe9yLvdyv2XvFGO+IMY6LMY4bMGBAK+Mo04UQqCgr8YmiJEmS1M7SLYo7SE0HbUphgzFpCSF8H7gKuCPG+MMm7sVe7tfqeym7lJeVsHj9djbvqE46iiRJkpS10i2KK0lNL22qvA0jNS21Kp0LhRCuB/4NuBv4h73ca/d1m7oXND0tVV1ARVn9e4rLfaooSZIktZd0i+Ir9WOPa3gwhFAIVAAz07lICOE64DrgHuCyvWxxMZ/UtNMPN/HZ8fXf07qfss+RpcWE4II2kiRJUntKtyg+AETgmj2OX07qfcH7dh8IIRwUQjh8zwuEEL4DXA/8GvhSjLGuqRvVb4PxOHBSCKG8wfk9gcuAN9lj9VV1Hb0L8zloQE+fKEqSJEntKC+dQTHG+SGEW4CrQgiPAP8LjAKuBp6j8aql04ARpPZdBCCE8FXgu8BSYCrw2RBCg1NYE2N8psGvvw2cCjwdQrgR2EKqlA4DJu3lSaS6iIqyEp5dtJYYI3v8dyRJkiSpDaRVFOtdA7wNXAFMAtYDPyW1ammTTwcb2L3v4XDgV018/hzwXlGMMb4VQvgI8J/At4ACYDZwZoxxaisyKwuVl5Xw0KzlrNi0k9I+rV1sV5IkSVJL0i6KMcZaYEr9V3PjDmji2MXAxa0JFmNcCHyiNeeoa6goTS1oM2fZJouiJEmS1A7SfUdRyhiHD+lFQV6OC9pIkiRJ7cSiqE4nPzeHMUN7M3fZ5qSjSJIkSVmpNe8oShnhnQ3b2VFVyxurN3HAt56gZ7c8Jh81lMsnjGREv6Kk40mSJEmdnk8U1an8ZdFazrxpOn9bs/W9Y9t21fDbl5dx5k3T+cuitQmmkyRJkrKDRVGdxjsbtvOVe2ezs7qWuj02SKmpi+ysruUr987mnQ3bkwkoSZIkZQmLojqNO6cvprq2+Z1Yqmvr+Pn0JR2USJIkScpOFkV1Go+9upKaPR8l7qGmLvLoqys6KJEkSZKUnSyK6jS276pJb1xVeuMkSZIkNc2iqE6jqFt6i/QWFbiYryRJkrQ/LIrqNCYfNZS8nNDsmLycwLlHDeugRJIkSVJ2siiq07h8wkjyc5v/TzY/N4fLJhzYQYkkSZKk7OQcPXUaI/oVcetFR/OVe2dTXVvXaGGbnADd8nK59aKjGdGvKMGUGW7jYphxM8x7EKq2QUFPGHs+jL8K+o5MOl3m55MkSeoiQozNryLZWY0bNy7OnDkz6RhqB+9s2M7Ppy/h0VdXsG1XDQEY3rcH91x6nCWxOW8+Aw9+AWqroa76/eM5+ZCbD+ffA4ecZj5JkqQsEUKYFWMct0/nWhTV2f3Lo/N57NUVzP730yjMz006TmbauBh+9hGo3rH3Mfk94MoXknlyl+n5JEmSOqH9KYq+o6hO74zRg9lRVctf31yfdJTMNePm1JO65tRWw4u3dEyePWV6PkmSpC7GdxTV6X14ZD96Febx5GurmXjEoKTjZKZ5DzaeztmUumqYeRe882LHZGpo3UKIdc2PqauGeQ/ApCkdk0mSJKkLsyiq0yvIy2HiqEFMXbiGmto68lpYGbVLqtqW3rhYB30TWDV27WvpjUv355AkSdJ+sSgqK5wxehCPvrqCl5dsZPzB/ZOOk3kKekLV1pbHdesFF9zX/nn29IPS9PIV9Gz/LJIkSfIdRWWHEw8dQGF+Dk+9tjrpKJlpzCeB0PyYnHwY+5kOifMBY89P3b9ZOXDkpzskjiRJUldnUVRW6FGQx4mHDOCp19ZQV5edK/nus52bYM0CoIV/L7n58OGvdkikDxh/Ver+zaqDVXNhy6oOiSRJktSVWRSVNc4cM5jVWyqZt2Jz0lEyx5aVcPdZsGoejP96aouJPZ/c5eSnjp9/T3JbT/Qdmbp/c/k+fBWsXQi3nQBvTUsmpyRJUhdhUVTWOPXwQeTlBJ5c4PRTANYtgl+cDpvegc/9Dk7/XmofwmO+mHoXMYTU92O+mDqe9Gb2h5zWfL4z/i9c/hcoGgD3ngfTvg+1NclmliTAf7iIAAAgAElEQVRJylIhxuycpjdu3Lg4c+bMpGOog33+F/+P5e/u5M/f/CghtPBOXjZb9jLcX//e3+d+B0Mrkk7Udqp2wJ/+CV69F4aPh0/9AnoPTTqVJElSxgkhzIoxjtuXc32iqKxyxujBLFm/nTfXduFtFBb9CX51DnTvA5c+nV0lEaCgB3ziFjj3jtQ7i7edAG9NTTqVJElSVrEoKqucfsQgQqDrTj+d9Sv47Wdh4Ci45Olk9kTsKOWfgSuehZ6DUlNRp37XqaiSJEltxKKorDKwdyFHD+/T9bbJiBGe/S94/Go46BT44uPQc0DSqdrfgEPhsmlw9BfgrzfArz4Om1cknUqSJKnTsygq65w5ejCvrdzCso07ko7SMepq4Y/XwrM/gPLPwoW/hW5daGP6gh5wzk/hk3emVne97QR485mkU0mSJHVqFkVlnTNGDwboGk8Vq3fCg1+AWXfDCd+AybemsR9hlhp7Pnz5Oeg1BO77FDxzHdRWJ51KkiSpU7IoKusM79eDUUN6Z39R3LER7pkMbzwBH/sRTLwutaVEV9b/ELh8GhxzMbxwE/xyEmxennQqSZKkTseiqKx0xuhBzHznXdZt3ZV0lPaxeTnc/TFYORs+fTd86MtJJ8oc+d3h7B/Deb+ANa+lpqL+7amkU0mSJHUqFkVlpTPHDCZGeOb1NUlHaXtrXoefnwZbVsJFj8Doc5NOlJmO/BRc8Rz0Lk3tKfn0vzsVVZIkKU0WRWWlwwb14oB+PXgy26afvv0C3H0mxDr40p/gwAlJJ8ps/Q+Gy56BY74EM34Cd58Fm5YlnUqSJCnjWRSVlUIInDF6MDPeWs/mnVnyFOn1P8Cvz4WiganyM3hM0ok6h/zucPZNqamoa1+H2yfAoieTTiVJkpTRLIrKWmeMGUxNXeQvb6xNOsr+e+XnqdVNh4yFS5+GkuFJJ+p8jvwUfPn51FTU33wGnv43p6JKkiTthUVRWauitISBvbrx5IJOPP00Rvjzf8AT34RDz4Av/AF69E06VefV7yC4bCqMuxRm/DS1INCmpUmnkiRJyjgWRWWtnJzU9NPn/raOnVW1Scdpvdoa+MNV8Px/w1Gfh8/cl9pcXvsnvxA+fgN86m5Y+wbcNgHe+N+kU0mSJGWUtIpiCCEnhHBtCOGNEEJlCGFZCGFKCKEozfO/HUL4XQhhcQghhhDebmbsL+vHNPX1qTR/LgmAM0YPZmd1Lc+/uS7pKK1TtQMe+By8ei+c+M9wzk8hNy/pVNllzCfhy8+lpvH+9kJ46l+hpirpVJIkSRkh3T953ghcDTwKTAFG1f/6qBDCxBhjXQvn/wDYCMwGStK85+ebOPZymudKAHxoZF+Ku+fz1GurOWP04KTjpGf7htQ7dCtmwaQb4NhLk06UvfodBJc+k3pf8cWbYemLqSeNfUYknUySJClRLRbFEMJo4GvAIzHG8xocXwL8BLgAuL+FyxwUY1xcf94CoGdL940x3tvSGKkl+bk5TBw1iGdeX011bR35uRk+2/rdd+De81LvzZ1/D4w6O+lE2S+/ECb9DxxwAvzha6lVUSf/DA6flHQySZKkxKTzp+YLgQDctMfxO4EdwEUtXWB3SWyNkNI7hJDhf7JXpjtj9CC2VNbw0uINSUdp3ur58IvTYfta+MLvLYkdbfTk1FTUPgfAbz8LT37bqaiSJKnLSqeEHQvUsce0zxhjJTCn/vP2sLn+a2cI4ZkQwofa6T7KciceOoDu+bk89VoGr3665PnUZvA5uXDJUzDiw0kn6pr6jkxNRT3uy/DSrXDXGfDu20mnkiRJ6nDpFMWhwPoY464mPlsB9A8hFLRhptWk3om8EjiX1PuN44DpIYSJbXgfdRGF+bmcdNgAnn5tDXV1Mek4H7TgkdR0095DU3skDhyVdKKuLa8bnPWj1NTfDW/BbSfCwsdh42L44zfgB6VwfUnq+x+/kTouSZKUZdJZzKYH0FRJBKhsMKZN5mjFGL+1x6HHQgj3k3p6+TPgkL2dG0K4ArgCYPhwNyTX+84cM5g/LVjNq8s2ccyIPknHed9Lt8GT34Lhx8OFv4HuGZStqzviEzB4LDz0JXjgIsjJgwjEmtTnVVth9j0w9zepUnnIaYnGlSRJakvpPFHcAXTby2eFDca0mxjjm8CDwMEhhEObGXdHjHFcjHHcgAED2jOSOpmTDx9Ifm7InOmnMcIz18GT/ye1aMrnH7UkZqK+B8Lk21Ilsa7m/ZK4W101VO+AB7/gk0VJkpRV0imKK0lNL22qLA4jNS21I1Z8eLv+e/8OuJeyTO/CfMYf1J8nF6wmxoSnn9ZWw2NXwgs3wbhLUk+j8rsnm0l79/IdpNbzakZtNbx4S4fEkSRJ6gjpFMVX6scd1/BgCKEQqABmtkOupuyecrqmg+6nLHPmmMEs3biDN1ZvTS7Erm1w/2dS0xVP/rfUPok5ucnlUcvmPZh6cticumqY90DH5JEkSeoA6RTFB0i9mXPNHscvJ/Vu4n27D4QQDgohHL6vYUIIRfUFdM/jRwGfBhbGGP++r9dX1zZx1CBCgCcXtPP0070terJ8Jvzq47D4L3D2T+Cj/wShhSdVSl7VtrYdJ0mS1Am0uJhNjHF+COEW4KoQwiPA/wKjgKuB54D7GwyfBoxgj3laIYTP1x8HGAAUhBD+rf7X78QYf13/z4cAfwohPAa8CWwHyoFLgFrqF6qR9sWAXt04dkRfnnptNdeettdXXffPm8+k3lerrX7/KVTVVpj1K5h5F+TmwwX3w2Efa5/7q+0V9Ez9b5jOOEmSpCyRzqqnkHqa+DapojYJWA/8FPhOjLEujfMvBT66x7Hv139/DthdFFcDU4GTgc8B3YFVpJ5q/jDG+EaaeaUmnTFmMN//4+u8vX47B/QvatuLb1ycKonVTazt9N4iKAEGHNa291X7Gnt+anXT5qafhlwY+5mOyyRJktTO0pl6SoyxNsY4JcZ4WIyxW4xxWIzxGzHGbXuMOyDG+IG5dDHGk2KMYS9fJzUYtzrG+PkY4+Exxt4xxvwY4/AY4xctiWoLpx8xCKB9Vj+dcXPqSWJzYp2LnnQ2469KPQluTqx1ewxJkpRV0iqKUrYo69uDMcN6t09RdNGT7NR3ZP3KtD0gZ4/CmJMPeYXQvS/8/muwwVeoJUlSdrAoqss544jBzF66iTVbKtv2wi56kr0OOQ2ufAGO+SJ065VahKhbr9Svv/IiXPJk6qniPZNh84qk00qSJO03i6K6nDPHDAbg6dfbeKeVdBczcdGTzqnvSJg0Bb69HK7blPo+aUrq+IDD4KKHYee78OvJsH190mklSZL2i0VRXc7BA3syckART7X1Nhljz//g1MQ95eS76Em2GnoUfPYB2LQU7v0kVG5OOpEkSdI+syiqywkhcMbowby4eAObdlS13YXHXwWhhd9Sufnw4a+23T2VWQ74CJz/a1jzGvzmQqjemXQiSZKkfWJRVJd05ujB1NZFpi1c23YX7dYb8rsDAcIeO8/k5KcWQzn/ntRURWWvQ0+Hc2+Hd2aktkupacO/jJAkSeogFkV1SWNLixlSXMiTbbX6aYzw+NdTeyh+9gEYd/EHFz258gW3UOgqjvwUfPxGePNpeOwfoK426USSJEmtktfyECn77J5++puXl7KjqoYeBfv5W2HO/fDGH+H0/4BDz0h9TZrSNmHVOY37Uuo9xanXpZ42f/zG1F8cSJIkdQI+UVSXdfroQeyqqeO5Rev270Lvvg1/+j9wwAQ43vcP1cAJ18AJ18Ksu2Hq9UmnkSRJSptFUV3WcQf0pU+PfJ7an+mndbXw6D+knhRNvhVy/C2lPZx6HYy7BF64CabfkHQaSZKktDj1VF1WXm4Opx0xiD/NX01VTR0FeftQ8mb8BJa+mFq8pGR424dU5xcCnDUFKrfAtO9CYTEce2nSqSRJkprl4w91aWeMHszWXTXM+Ps+bJC+ah78+f/CEZ9wb0Q1LycHzr0NDjkDnvgmzH8o6USSJEnNsiiqS/vIwf0pKsjlqdfWtO7E6kp45Aro0Q8+fpOLlKhluflw/q9gxHh49Mvwt6eSTiRJkrRXFkV1aYX5uZx0+ECeeX01tXUx/RP//H1YtxAm3wI9+rZfQGWX/O5w4W9h0JjUHotv/zXpRJIkSU2yKKrLO3P0YNZvq2L20nfTO2Hxc/DizXDs5XDwxPYNp+xT2BsuegRKRsD9F8CK2UknEvDE4ic4/aHTGfursZz+0Ok8sfiJpCO9J5OzSZKyl0VRXd7Jhw+kIDeHJxeksfrpzk3w2JXQ72A47XvtH07ZqagffP5R6N4H7j0P1i1KOlGX9sTiJ7h+xvWs2r6KSGTV9lVcP+P6jChkmZxNkpTdQoytmG7XiYwbNy7OnDkz6RjqJC755SssWr2Vv/6fkwnNvW/48OWw4GG47BkYdkzHBVR22vB3uOtMyMmDS56EPiOSTtQlnfLgKazb+cH9VHNCDgO6D0gg0fvW7VxHXaz7wPFBPQYx9dNTE0gkSepMQgizYozj9uVct8eQSE0//fMba3lt5RbGDCtuetCCh2H+g3DSv1gS1Tb6HZR6svjLs+CeT8AlT0GvQUmnynoxRha9u4ip70xl2tJpTZZEgLpYx/ih4zs4XWOPvvVok8fX7FjDJU9dwoRhEzix9ERGFo9s/i+5JElqJYuiBJw6aiA5AZ56bXXTRXHLSvjjN2DYOJjwzY4PqOw1eAx87uFUUfz1ufClJ1JTUtWm6mId89bNY+o7U5m6dCortq0gJ+Rw9MCj6V3Qmy1VWz5wzpCiIXzvI8lOMX9p1Uus2r7qA8eL8ovYtGsTN8y6gRtm3cDQoqFMKE2VxmMHH0v3vO4JpJUkZROLogT069mN4w7sy1Ovreabpx/W+MO6OnjsK1BbBZ+8A3L9baM2VnYsXHAf3H8+3Pdp+Pxj0K1n0qk6veq6amaunsm0pdOYtnQa63euJy8nj+OHHM/lR17OSWUn0a97v/feA6ysrXzv3MLcQr5+9NcTTJ/y9aO/3mS2fz/+35k0chKrt6/m+eXPM33FdP7w9z/wwKIH6JbbjWMHH8uJpScyYdgESnuVJvgTSJI6K99RlOr98oUlXP/460z75kc5aECDP6T/v9vhT/8MH78Rxl2SXEBlv4WPp7bNOPBE+OyDkNct6USdTmVNJTNWzmDa0mk8u+xZtlRtoXted04YdgITh09kQukEehX0+sB5Tyx+gh/P/jGrt69mcNFgvn7015k0clICP8EHpZttV+0uZq2exfMrnuf55c+zbOsyAA4sPpATh53IiaUnctTAo8jPze/oH0GSlJD9eUfRoijVW7lpJ+P/88/885mH8ZWTDk4dXLcIbj/x/T+4+w6Q2tuc+1Mr6x7+cfj0r3yCnYZtVdt4fvnzTF06lb+u+Cs7a3bSq6AXJ5edzKnDT2X80PEU5hUmHbPDvb35baavmM7zy59n5pqZ1NTVUJRfxPih45kwbAInDDuBAT2SXaxHktS+LIpNsChqX3zi5r9CCPz+qx+Bmir4xUTYvByufNFFRtRxXvoZPPktqPgcnHMz5LiT0Z42Vm7k2WXPMvWdqby06iWq66rpV9iPU4efyqkjTuXYwceSn+OTs922V2/npVUvMX35dKavmM7aHWsBGNV3VGqKaukExvQbQ25ObsJJJUltyVVPpTZy+ujB/PdTi1i1eSdDZk2BVXPhM/daEtWxjr8SKjfDsz+Ebr3hzB/6NBtYvX31e+8bzlozi7pYx7Cew7jw8AuZOGIiY/uPtejsRVF+UapEDz+VGCN/e/dv773beOf8O7l93u306daHjwz7CCeWnsj4oeMp7raXFaAlSV2CTxSlBv6+bhunTnmOW0+s4axXLobyz8LkW5KOpa4oRnjqX+ClW+Gkb8NJ30o6USLe3vz2e+Vw/vr5ABxUfBCnjjiVicMncnjfw90WYj9tqtzEjJUzeH7F87yw4gU27dpETsihYkAFE0onMGHYBA7tc6j/niWpE3LqaRMsitpXZ095kjt3XMPgXvnwDy9AYe+kI6mrqquDP1wFc+6DM/8z9aQxy+3e43Da0mlMfWcqb216C4DR/UYzccREThl+CiOLRyacMnvV1tUyf/18pq+YzvTl01m4cSEAg3oMeq80Hj/keHrk93jvnExeCEiSujqLYhMsitpXc2/9Ikeu+T3bPvt7eh/20aTjqKurrYGHLk6tiPqJW+GozyWdqM3tbY/DowYexcThEzl1+KkM6Tkk6Zhd0toda/nrir8yffl0ZqycwY6aHeTn5DNu0DgmlE6gLtZx86s3f2D7juvHX29ZlKQMYFFsgkVR+2TRn+A3F/CzmrPpN/mHnD+uLOlEEtTsgvs/A0ueS62EesQ5SSdqtT2fOl1VcRUDegxg2tJp/Hnpn1m3c917exxOHD7xvT0OlTmqa6uZvXb2e+82Ltm8ZK9jhxQN4elPPd2B6SRJTbEoNsGiqFbbtg5+9mFiz0GcvOk7HDSkL7+4+NikU0kpVdvhnsmwag589gE46JSkE6WtqQ3td9u9x+Gpw0/lxNITm9zjUJlp2dZlnPXIWXv9fP4X53dgGklSU/anKLrmugSphUMe/zpUbiF88k5OGVPG9LfWs21XTdLJpJSCIvjcg9D/UPjt52DZy0knStuPZ/+4yZLYp1sfnvvMc9xw0g1MGjnJktjJlPUqY0hR01OC83Py+euKv5KtfxktSV2BRVECePVeWPQETLwOBh3BmWMGU1VTx7OL1iadTHpf9z5w0SPQazDc9ylYvSDpRC1atnUZq7avavKzTbs20T2vewcnUlv6+tFfpzC3sNGxvJBHj/weXDn1Si544gKmLZ1GXaxLKKEkaV9ZFKWNS1Kbmx8wAT6UWlXymBF96FdUwFOvrUk4nLSHXoPgC7+H/CL49bmw4e9JJ2rS9urt/Hj2j5n82GQCTW+rMLhocAenUlubNHIS14+/niFFQwgEhhQN4T9O+A/+8um/8N3x32Vr1Vau+cs1nPeH8/jTkj9RW1ebdGRJUpp8R1FdW10t3H0WrF0IV74AJe8vXvPtR+bxhzkrmfXvp1GY7ybeyjDrFsHdH0sVxkuehOJhSScCUiuYPv73x/nx7B+zbuc6zh55NmP6j+HGWTe6MmYXVFNXw5NvP8md8+5k8ebFHND7AC478jLOGnkW+Tn5SceTpKznYjZNsCgqLdOnwLTvwSfvhLHnN/roL4vW8qW7X+Gui8dxyuGDEgooNWPlq/DLs6H3EJj8M5hzP8x7EKq2QUHP1H/T46+Cvh2z7+CctXP4r5f/iwUbFjC2/1j++bh/pnxAOeBee11dXaxj2tJp3DHvDt7Y+AbDeg7jkjGXMPngyRTkFiQdT5KylkWxCRZFtWjVXLjzFBh1DnzqLgiNp8ftqqll3PenctaRQ/ivT41NKKTUgrdfgF9PhtpqCLkQGyzAlJMPuflw/j1wyGntFmH19tXcNPsmnlj8BAO7D+SaY65h0shJ5ATfblBjMUaeX/48t8+7nfnr5zOwx0C+NPpLnHfoeb6vKkntwFVPpdaq3gmPXAFFA2DSlA+URIBuebmcfPhAnlm4hppaF2JQhuo9BAhAbFwSAeqqoXoHPPgF2Li4zW9dWVPJbXNv45zHzuGZt5/h8iMv5/FzH+fsg862JKpJIQQ+WvZR7jvrPu447Q7KepXxX6/8F2c+fCZ3LbiL7dXbk44oSarn/5Ora5r2PVj3Bky+FXr03euwM8cMZuP2Kma+826b3Xr3U/yGT/N31VhEtY9m3AwtrShZWw0v3tJmt4wx8uSSJznnsXO4Zc4tnDDsBH4/+fdcffTV9Mjv0Wb3UfYKIfDhoR/ml2f+krvPuJvD+x7OjbNu5PSHTudnc3/G5l2bk44oSV1e2kUxhJATQrg2hPBGCKEyhLAshDAlhFCU5vnfDiH8LoSwOIQQQwhvtzD+QyGEqSGErSGELSGEJ0MIFenmlfZq8bPw0q1w3Jdb3LT8o4cOoFteDk8uWN1mtw/1Ty9Dg6eY9yzczO/+tqXN7qEuZN6DqSeHzamrhnkPtMntXt/wOhc/eTH/9Pw/0bugN3edcRc3nHQDpb1K2+T66nrGDR7H7afdzv1n3c/Rg47m1jm3cubDZ/KT2T9hY+XGpONJUpeV14qxNwJXA48CU4BR9b8+KoQwMcYWN0n6AbARmA2UNDcwhHA88CywAvhO/eGrgOkhhPExxvmtyC29b+e78OiVqU3LJ17f4vCibnlMOGQAT7+2muvOPqJRuWut2+e9y6ZdtRxYnE8gMLZ/NyIwsEceq3fUMKhHa347SvWqtrXtuL1Yv3M9P331pzz65qP0KezDdR++jnMPPpfcHFcEVts4csCR/PSUn7Jo4yLunH8nP5//c+5deC+fPvTTXDz6Ygb0GJB0REnqUtL6k2kIYTTwNeCRGON5DY4vAX4CXADc38JlDooxLq4/bwHQs5mxPwGqgBNjjCvqz3kQWEiqpJ6eTm7pA574R9i+Fi68HwrSmyJ35pjBTF24hvkrNjO2tNm/42hSXYzkhMAJw7oTI7y+cRe9CnK4ee5GFm6soiA3cMaIIk4pS+vhvNRYQU+o2preuH1QVVvFfQvv4/Z5t7OrZhdfOOILfLn8y/Qq6LVP15Nacljfw/ifj/4PiysW8/N5P+e+hffx2zd+y7mHnMulYy5lSM8hSUeUpC4h3UcYF5JaLeGmPY7fCfwncBEtFMXdJbElIYSDgWOBu3aXxPrzV4QQfgd8KYQwOMbYdnMB1TXMfwgWPASn/BsMPSrt0yaOGkhuTuDJBav3qSjm1D+FHN2vEIAx/QtZuHEXBxYXcFifbnzioF6U9XI/Me2jsefD7Huan34a8mDsZ1p12Rgjzy57lv+Z+T8s3bqUE0tP5B/H/SMHFh+4n4Gl9IwsHskPJvyAK8uv5BcLfsHDbz7Mw397mHMOPodLx1zK8N7Dk44oSVkt3XcUjwXqgJcbHowxVgJz6j9vK7uv9WITn71EqrAe04b3U1eweQU88Q0oPQ4+cm2rTi3pUcDxI/vy1Gtt83cTL63awTPvbGN4r3w+fUhvynrlUxcjdVm6VY3a2firUltgNCvCh76c9iXfevctvvzMl7n6L1eTl5PHbRNv45ZTb/n/7N13eFRl2sfx7zMlPYEkEAKhdwiGjlIFlKKAFEF0V0RdhRVQrKuuLZZ1fd21YF97QUFEihhpKggCinTpJRAIBAKEkJ5Med4/ThISGEKAJGeS3J/rmmsyp809aMrvPE1CojBFg5AGxPaIZeGohdzU6ibi4uMYNm8Yj618jH2p+8wuTwghqqzSBsV6wAmtda6HfYeBWkqpsloxt16R63p6L4AoTycqpSYopdYppdYdP368jMoRlZ7bDfPuAZcTRr4H1osfCzg4OpJ9xzPZm1yKLn4lyHG6+XT7aRoG27m+cRB1Ao1aLEoVtjwKcVHCmhrrJNoDjHUTi7LYjYd2wfKXjO+BEpzOPc2Lv7/I6AWj2XpyK491e4zZN8ymZ1TPcvwAQpROZGAkj1/5OItuXMRtbW/j54M/M3L+SB5c/iA7U3aaXZ4QQlQ5pQ2KAYCnkAiQU+SYslBwHU/vV+J7aa3f11p30Vp3qV1bBr2LfGvfh/2/wOAXIbzZJV1iQNtIgMua/dStNX42C9OursOI5iEE2C3FlsgQ4pK1GAD3rILO48E32FgX1DfYeD1lLVz7LGz9FuZO9BgWnW4nX+34iuvnXM/Xu75mdMvRxI2M469t/or97PAphMlq+dfioS4PsfjGxdwdczdrjqxhzIIxTPlpCluObzG7PCGEqDJK27SSBUScZ59fkWPKQsF1fCvgvURVl7wTfnwGWg6GTuMv+TKRNfzo2LAmi7cdY0r/Fpd0jYIWQ1+bBbfWKIovkZGc5SQiwFY4+Y0QFyWsKQx5xXicrdf9gIYfY43XI/9X2LK++shqXl77MvtO7+PKulfyj67/oGVoyworW4hLFeoXyr0d72V89Hhm7pzJF9u/4K8//JWr6l7FhJgJdI0sy1ExQghR/ZQ2KB4B2iqlfD10P43C6JaaV0Y1HSly3bMVbPPULVWI4px5MOduY7bHG940Wlkuw6DoSF5auJPEU1nUD728BnSLUoWtiXtO5RLqZ+Wp1cn879p6EhJF+eiVPzb3x1hQioT+j/PfDa+zPHE59YPqM63fNPo16HdZS8AIYYYQnxAmxEzg1ja38s3ub/hk6yfcufhOOkV0YmLMRFJyUnhj4xsczTxKZGAkUztNZUjTIWaXLYQQXq+0XU//yD+2W9GNSik/oAOwrgxr+iP/ubuHfVcBGlhfhu8nqqpfXoKjW+CGNyDofA3ipTco2uh+umTbscu+FhitiW6teX7tCQJsFuoH21l5OBNAJrYR5aPXA2T0e5xXE5cy4ruRrD26lgc6P8D8EfPp37C/hERRqQXYAxgfPZ5FNy7i8W6PczjjMBN/nMg/f/0nSZlJaDRJmUnEro4lLj7O7HKFEMLrlTYofo0R0O4/a/vdGOMFvyzYoJRqppRqfakFaa33YgTPMUqpgoltyP96DPCzLI0hLujgb/Dra9BxHLQumzvHTWoF0joymEVlNPtpQRfT/vUDmbsvnVta1WDePmOyHGlVFGXN5XYxZ88chhxdyKc1Qxiank6cTyvubDseH2tZzUUmhPn8bH78pc1fWDhqITV8aqApfuMtx5XDtA3TTKpOCCEqj1J1PdVa/6mUehuYopSaA/wAtAHuA36h+BqKPwGNMJaxKKSUGpe/HaA24KOUejL/dYLW+osih08FlgErlVJv5m+7FyPYPlTKzyaqq9x0Y9KOGg1g8L/L9NIDoyN56+c9nMjIpVaQp2G0pVfwDTK6RQgPrjjK2JYh+FoVG5Oz6RjhL2MVRZlZf2w9/7f2/9iRsoOOER1555p3iN6xCH56DiwTjTGLFqvZZQpRpuxWO5DTyZAAACAASURBVGl5aR73JWUmVXA1QghR+VzMOgH3AweACcAQ4ATwJvC01tpdivP/Blx91rbn859/AQqDotZ6tVKqL/BC/kMDq4ExWuvNF1GzqI4WPQ6pB+GOhcbMj2VocHQkb/y0hx+3H+Pmbpe32HNB19MgHwsxtfxYeCCDG5uHMH3naTpG+EtIFBctLj6OaRumFY7Fuq3tbWw6vonFBxZTJ6AOL/d5mcGNBxtdTHtHGyf99BygjKVjJCyKKiYyMPK8ofDV9a9y9xV3E+xTtr8nhBCiqlBVdXr+Ll266HXrynLopKgUdsbBzL9Arwfh2mfK/PJaa/r8ZxnNagfx6R3dLnxCKa6nlCIp08E/VyXzycAovtmdxpAmQQTYS9szXAgjJMaujiXHlVNsu91i5+4r7ub2drfjb/M/98QV/4Wfn4eYsTDiXQmLokrx9H3ha/ElulY0G5M3UtO3JpM6TGJ0y9HYLBe/xq4QQng7pdR6rXWXSzlX/hIVVUdGMnx3H0TGQN/Hy+UtlFIMjo5k9d6TpOU4yuR6bq2pG2hnXJuapOa4GNEsWEKiuGjTNkw7JyQChPqGck+HezyHRIA+D0P/J2HL1zDvHnC7yrlSISrOkKZDiO0RS93AuigUdQPr8mzPZ/nsus+YOXQmzUOb86/f/8Wo70bxy6FfZG1bIYQoQm6fiapBayMk5qbDqA/AVn6TcwxuF8kHK/ezbGcywzt4WsXl4hR0Me1bP8Bjd9Nsp5uUHBdRQbLwuTi/83WvO559/MIn93nEeP75BUDBiHekZVFUGUOaDvG4HEbb8LZ8NPAjlh9azqvrX2XKz1O4su6VPNLlEVqFtTKhUiGE8C4SFEXlkxIPq9+CLbMgL8NYJ7Fue0j4FQa/BBGXPOluqXRsEErtYF+WbDtWJkGxgKeQ6HBpVh7OIm5/BtP6RpbZe4mqZWXiSizKgtvDcPHIwFL+f9PnEWM0+LIXjNcSFkU1oJSiX8N+9Krfi292fcO7m99lzIIxDG8+nHs73ktEwOUvrSSEEJWV9G8TlcuepfBuT9jwOeSlA9p4TvgVlAXCmpZ7CRaLYmDbOizblUyOo2y76Z3d7cluVVwZ6c/+tDyWHcos0/cSlV+WI4vn1jzHpJ8mUdu/Nj6W4i3pflY/pnaaWvoLXv0I9HsStsyE+ZOlG6qoNuwWO39p8xfiRsUxPno8cfFxDJ07lHc3vUuWI8vs8oQQwhQSFEXlkRIPs24DRxa4PYwP1G745nbjuHI2KDqSrDwXK/ecKLNrHjidR4bjTIvQ0Uwnn2xL5Z+rkokO86VxiHQ9FWdsSt7E6AWjmb17NrdH307cqDie6/lcsbFYsT1iPXa5K9HVj0C/J2DzDAmLotoJ8QnhoS4PMX/EfHpH9eadze8wbO4w5u6Zi0u+F4QQ1YzMeioqj+8fNFoSPYXEAhY7dB4PQ14p11LynG66vLCUgdGR/HdM+zK55lc7T3M828kdbWvy+Y7TbDyeQ7Madka3CKFl6OWt2SiqDofLwbub3+WjrR8RGRDJC71eoGtk17J/o19ehmX/gvZ/geFvSTdUUS1tSt7Ef/74D1tObKF1WGse7vIwV9a90uyyhBCi1C5n1lMJiqLyeLF+fnfTC/ANhscTy72cB7/exM+7kln3xLXYrJfeOF+wRMbpXBe3LDxMLX8r3er4M7xZMA2Cz7QiurWWtRWrub2n9vLPX//JjpQdjGg+gke7PkqQT1D5veHy/4PlL0pYFNWa1ppFBxbx+vrXOZJ5hKvrX82DXR6kaY3yH+oghBCX63KCokxmIyqPvIyyPe4yDYyOZM7Gw6zdn0KP5rUu+ToFS2TU8LXSJyoAmwWmdAgDjD9QNMZENxISqy+3dvPF9i94Y8MbBPkEMa3fNPo37F/+b9z3UeN5+YugFNzwpoRFUe0opbiuyXX0b9ifL3d8yQdbPmDU/FGMbjmaSR0mEeYXZnaJQghRLmSMoqg8SttyUp4tLEVc3bI2fnYLi7YdLbNr3hldkwh/Gy63LmxplIBYvR3JOMJdS+7iv+v+S4+oHsy5YU7FhMQCfR811iXd9KWxBI373JlVhagOfK2+3NnuTuJGxTG6pTE+eMicIXy89WNyXblmlyeEEGVOgqKoPGJuMsYglsRih5ixFVKOv4+Vq1vWZvG2o7jdl9eFuyAMRgTYGN0iBKtFoSQgVmtaa+bvnc+N393IthPbeK7Hc7zR7w3C/cMrvpi+j8HVj8Gm6fDdvRIWRbUW5hfGk1c9yZwb5tC5TmdeW/8aw+cNZ9H+RefMXC2EEJWZBEVRefSYYiyBURKrHbpPrph6gMHtIjmWlsvmxNQyu2aAXb4tq7uUnBQeWP4AT656kpahLfn2hm8Z2WKkuTcP+j3uVWFRHzti6vsL0bRmU9665i0+GPgBQfYgHlnxCLcuvJVNyZvMLk0IIcqE/EUqKg+rL9h8AQXqrOG1FjvYA+CmzytkLcUC/VvVwWZRZdr9VFRvvxz6hVHzR7EicQUPdn6Qjwd9TP3g+maXZfCSsKi1Rv88H/fCWWhp3RQmu6ruVXw99Gue6/EcSRlJjFs4jod/eZjE9PKfVE0IIcqTBEVROTjzjDUStRvGzYEutxuzmyplPHceD/esghYDKrSsGgF2ujcLZ/HWo9LlSFyWTEcmsatjmfLzFML9w5kxZAZ3tLsDq7dNHtPvcbj6USMsLqjYsFjwPaaUQjVrC1qjLPJrTJjParEyssVIvh/5Pfe0v4cViSu4Yd4NvLLuFdLy0swuTwghLonMeioqh6VPQeJaGPMZNOtvPMp5rcTSGtwukifmbmX3sQxaRQabXY6ohDYc28ATvz7B4YzD3NnuTiZ3mIyP1cfsss6v7+PG8y//ZzwPexPKMbBptxtlsaCUQqccR2/fiF6xEMtNdxv78yd+EsJsAfYAJnWYxI0tbuStTW/x2bbPmLd3Hve0v4cxrcZgv9A4eyGE8CJyK1Z4vz9nw+/vQfcpED3C7GrOMaBtHZSCxdL9VFykPFcer61/jdsX3Y5G8+ngT3mg8wPeHRLBaMnv+zj0+QdsnA4Lynk2VKcDfSQB93dfohd/i146B9U6BtW8rYRE4ZXqBNbh+Z7PM2vYLFqFtuLfa//NqPmjWHZwmfQ+EUJUGtKiKLxb8k5jSv6G3eHaWLOr8Sgi2I/ODUNZtPUo913TwuxyRCWx+9RuHl/5OLtP7ebGFjfySNdHCLQHml1W6SkF/f5pfL3iZeN52Btl3rKoE/aif5oPteuiGjUHH18IDEZ17lWm7yNEeWgd1poPBn7AL4m/8Mq6V7hv2X10i+zGw10epk14G7PLE0KIEklQFN4rNx1mjQOfQBj9iTGjqZcaFB3Jv37YwaGULBqEBZhdjvBiLreLL7Z/wRsb3yDYJ5g3+79J3wZ9zS7r0hSGRQ0r/mO8HjqtbMNieASq29Wodl0A0OtWgr8/BJ2/m3dBV1UhvIFSir4N+tIzqiezd8/m3U3vMvb7sQxrNozo8Gg+3fYpRzOPEhkYydROUxnSdIjZJQshBCBdT4W30tqYVfHkXhj9MYTUNbuiEg2KjgSk+6koWWJ6In9b8jdeWf8Kfer3Ye7wuZU3JBZQCvo9Ab0fhg2fw/f3l1k3VK01KijkTEjMy0Xv34UKrY2qEZb/9ka3U711HXrz78Y2i0VmQxVex26xc0vrW4gbFcft7W4nLj6Of6/9N0mZSWg0SZlJxK6OJS4+zuxShRACkKAovNXv78G2uXDNM9Ckt9nVXFDD8ADa1g1h0VYJiuJcWmvm7pnLjd/dyM6UnbzQ8wVe6/saYX5hZpdWNpSC/k/mh8XPyiwsnjP20OkAtwtiugGgXS7j2emA+k3Q61fi/m56YYui1lrGgwmvE+wTzIOdH/T4/Z/jymHahmkmVCWEEOeSoCi8z8HfYMmT0Hoo9JxqdjWlNig6kvUHT5GcnmN2KcKLnMw+ydRlU3l69dNE14pmzg1zGN58eNWbgKUwLD5khMW4B8p8ghsVEIRl7ESUj68RBq3G0iE6biZ6029Y7nwYgmuiP/g/9IHdxjIaVe3fWVQZJ7JPeNyelJmEW0uLuBDCfBIUhXfJSDbWS6zZEEa8Y/zxWUkMbheJ1rB0+zGzSxFe4ueDPzPqu1GsOryKh7s8zIcDP6ReUD2zyyo/SkH/p4ywuP7TMg+LRVsHi45BVENuhlMncH/xBqpzT9TQW9ALvkKvXnrm3Pw69JEEdK7czBHmiwyMPO++sd+P5dfDv0qLuBDCVBIUhfdwOWH2nZCdCjd9AX41zK7oorSsE0Tj8ADpfirIyMvg6VVPM3XZVCICIpg5dCbjo8djUdXgR25BWOz1YH5YfNAYa/z9g/BifYitaTx//yCkxF/kpc+9caTdbpTNjmXkeFRMN/SXb0PyEdSkp6BuQ7Qj70xX1PTTuD95Ff3ei+i928roAwtxaaZ2moqf1a/YNl+LLze3upn0vHTu+fEe7lx8J5uPbzapQiFEdSezngrvsewFOLASRrwHke3MruaiKaUY1C6Sj1bu53S2gxr+3jtLqyg/646u48lVT5KUmcTdV9zNPe3vwe7FM/aWC6XgmqeNr399FTZ+ARrQTmNbXrox8c3mGXDT59BiwKW/Vf7ENcpiQbW/Cpq2QX/7CcrlQnUpPr5Zz/sM1ec6VMPmRnfVvduxDB5zye8txOUomN102oZp58x66nA5mL1nNu9tfo9bf7iV/g36c1+n+2hWs5nJVQshqhNVVbs1dOnSRa9bt87sMkRp7YyDmX+BznfAsNfNruaSbTx4ipHvrOa1se0Z2bG+2eWICpTnyuPNjW/y2bbPqB9cnxd7vUiHiA5ml2Wuk/vg7W7gdp7/GHsA3LMKwppe9tsVXRZDp6WiQmqe2bd9I+6v38fy0IuokFC0Iw8OxaOatr7s9xWivGQ5svhi+xd8su0Tsp3Z3NDsBia1n0TdIO+eCVwI4T2UUuu11l0u5dxq0A9KeL2T+2DuPVCvIwx+yexqLkv7+jWpE+LL4q0yTrE62ZWyi5vjbubTbZ8yuuVoZg+bLSERYM3bRktiSVwO47gyUHRZjIKQWHgztEkrVN/r0V+8hT6wB2X3KQyJVfWGqaj8AuwBTGw/kYWjFnJrm1uJi49jyNwhvPzHy5zKOWV2eUKIKk5aFIW58rLgowGQdhgm/AKhjcyu6LI98PVGvtuchJ/NQlaei0BfGyM61uPu3k1pFB5odnmiDLncLj7Z9glvb3qbmr41ebbHs/Sp38fssrzHi/WNbqYX4hsMjyeWSwk6Lxfl43vm9Zqf0I48LH2uK5f3E6I8JWUk8c7md/hu33f42/y5Pfp2bmt7GwH2ALNLu2zOzMPYAqPMLkOIKudyWhRljKIwj9YQ9xAc2wZ/nV0lQuKyXcnEbTmKy63JzDPWeMvIdTJz7SG+XX+Yd27tRL9WESZXKS5VXHxc4XiiWv61CLAHkJCWwIBGA3jqqqcI9Qs1u0TvkpdRtsddJO12o39dDPUaolobLbw67RRY8pfV0FqWzxCVSt2gujzf83luj76dNza8wdub3mbGzhlMjJnImJZjKu14aK3dZB9aDMpGUPOxKKvvhU8SQpQ76XoqzLPhM9j8FVz9KLS41uxqLlvCyUwmTd9Anuvc5QCcbk22w8Wk6RtIOJlpQnXicsXFxxG7OpakzCQ0muPZx0lIS2Bsq7G8cvUrEhI98Qkq2+MukrJYUPUaopd9j/un+biXLYDMDFSkMX5YQqKorJrVbMa0/tOYfv10mtZoyr/X/pth84bxffz3lXINRqUsBDQahjs3BZTV7HKEEPkkKApzHN4APzwCza6Bq/9hdjVl4oOV8Tg8hMSiHC43H67cX0EVibI0bcM0clznrr+3InGFBI7zibkJLBdq4bDAFeU386hq3QF1x0OQmwNOB6pTD2h5BSBjE0Xl1752ez4e9DHvXvsuQfYgHl/5OGMWjGFF4opK8f+3zg+17rw0sg//BMqKstgKtwshzCVBUVS8rBSYNR6C6sCoDwq7gVV28zYeweku+Rez062Zu/FwBVUkyorL7SIpM8njvqOZsm7mefWYAhfsCueGIxvhdDmNUXS7UX7+WK4fi7p2JKpxS5SvsXadBHxRFSil6BXVi1nDZvF/vf+PLEcWk3+azO2LbmdT8iazyyuRUhZcuSlkxn9LTtKv+Nbu5PE4rd0SHoUwgQRFUbHcbpgzATKOwk2fQWC42RWVmczcEpYAKHpcXumOE95hX+o+blt023n3RwZGVmA1lUxYU2OdRHvAuS2LFruxvcdUOLEH3usFuxaVeQnKYqkULStCXC6LsnB90+v5bsR3PHHlEySkJTBu4Tju/fle9p7aa3Z5HuWd2knmnplYA+rgG9EFa4Dx81Sp4t+3SllQKn/pG+2W72khKogERVGxVv4X9i41lsGI6mx2NWUq0Ld0c0MF+sgcUpWBw+Xg3c3vMnrBaA6mHWRsq7H4WopPsOBn9WNqp6kmVVhJtBhgrJPYebwxu6lSxnPn8cb2gc8ZMx7XqA8zxsLiJ8CZV6YlFLQcSguiqA7sVjs3t76ZH0b9wL0d72Xd0XWM+m4UT/z6BEcyjphdHmB0+86Mn4Mj5U/8ovrhW+cqlC0AirQaKqXQrlxSN/2HjD0zcKTty99uKfa9XNDS6Mo5gSvnZMV+ECGqOFkeQ1ScvT/B9BshZiyMfM/4g7EKeXLen8xce6jE7qc2i+KWbg15fkS7CqxMXKwtx7fwzOpn2Ju6l+uaXMejXR8l3D+82KynkYGRTO00lSFNh5hdbtXgyIElT8IfHxg3kUZ/DKGNza5KiEovNSeVD//8kBk7Z6DRjG01lrtj7ibML8y0mtyOTLISFhDQeDgWmz/OjESyD/9EQMPrsPpHoLULpaxoVx4oRd7JLeQm/47bkYm9Ziv8Intg9atV7JrZh5eTk7QcZQskuM3fsPqa9/mE8CaXszyGBEVRMVIPwf/6QHBduOtH8Kn8az6dLeFkJoNfX0m2w3XeY/ztVhbd31vWU/RSWY4s3tz4Jl/u+JKIgAieuuoprm5wtdllVS/b58P8e42vh78JbYebW48QVcTRzKO8s+kd5u+bj7/Nn/HR47mt7W0E2s3/feRIP0Dm3pnU7PhYse0Ze2bgyj6GX2QPfMI7oF255Bxbjc5Lw7/+QCy+NQCjhVI7s3DnnCB950fU7Pw0ymIr3Ce9CUR1JkHRAwmKXsSZC59cZ4xDmrAcwpuZXVG5WbYrmUnTN+BwuYu1LCpAAw8PasmUfi1Mq0+c35oja3h2zbMczjjM2FZjub/T/QSV07IN4gJOHYDZd8Lh9dD1bhj4Atj9zK5KiCohPjWeNza+wU8HfyLML4wJMRMY03IMPlafCqtBa3fhmMMC7rx0LD7B5+xzpB0gN/k3nOkHsAbUxTeiGz6hbTxeN+vgQlw5JwlueWv+NdPIOfILuSc2YAtpRmDjG7D4hJTfBxPCC0lQ9ECCoheJewj++BDGToc2w8yuptwlnMzkw5X7mbvxMJl5TgJ9bAy5oi5rD6RwIiOXuZN60Dwi2OwyRb7Tuaf5zx//Yf6++TQOaUxsj1g616la42crJWce/PQsrHkLIq+A0Z9CreZmVyVElbHl+BZe3/A6fxz9g6igKCZ3mMz1Ta7H6iUzkXtqCcw9sQnHqW34RfbCFtyo+PFuB2l/vol/w+vxCW2N25lN1oH5oF0ENhtL5r5vsAbWw7+e9BIR1YsERQ8kKHqJzV/D3AnQ4z4Y+LzZ1Zgq8VQWI95ehb+PlXmTehIe5Hvhk0S50VqzJGEJ//7936TmpnJHuzv4e/u/42uV/y5eZdcimPd3cDlg6OsQU35rLgpR3WitWX1kNdM2TGNHyg5ahLZgasep9Knfx2u6axZMVnN2C6Sx70yYdKTuJnP/XGp2fBSAvJRt5CavJaDxMKx+tchKiAM0AY2GSndUUa1cTlAs9aynSimLUuoBpdROpVSOUuqQUuoVpVSpOrdfzPlKqeVKKX2exyV9UGGCY9tgwVRo1BOuecbsakxXPzSAD27rQnJaLhO/WE9OCWMZRflKzkrm/mX38/AvDxMREMHMoTOZ2mmqhERv1Gow/H2V0ao45y6YPwXyssyuSogqQSlFz6iezBw6k5f7vEyOM4cpP0/h9kW3szF5I3HxcQycPZCYz2IYOHsgcfFxJtRYfGmMAmeHvbyUrdhrGEM73I4MXFlHsPrXxupXC+12YvGtCSi02ykhUYhSKnWLolJqGnAfMBdYCLQB7gVWAtfqC6yEejHnK6WWA9HAAx4u9YPWOuVC9UqLosly0uD9vpCXARNXQnAdsyvyGnFbkpj81QaGd6jH62M7yC+sCqS15ts93/LqulfJc+cxucNkxrUdh80iS5Z4PZcTlv8bVr4CtVvBmE8hwvM4JSHEpXG4HczZPYf3trzHiewTWLDg5syfd35WP2J7xHrNbM9aa7LiZ6NsAeSe2EiNK6Zi8QnG7cgg68B87GHt8A1vjysnhdxjq1G2IPyj+kqLoqhWLqdFsVR/HSmlojFC3Ryt9Y1Ftu8H3gBuBr4q4/MztdbTS/k5hDfRGuZPMiakuP17CYlnGRJTlwMnW/GfxbtoWiuIqdfK5DYV4WDaQZ5d8yxrj66la2RXYrvH0jCkodllidKy2uCap6BxT5gzAd7vB9f/BzreWuWW2hHCLHaLnbGtxzKs2TCu/eZa0h3pxfbnuHKYtmGa1wRFpRQ+tTqSk/QL7pwTZOydQWDTUVh8w3Ck7iKg8QgAXJmHcTsy8AuLKTxPCHFhpe16egvGxI2vn7X9AyALuLU8zs/vrhqi5Du6clnzFuxYAAOeg0Y9zK7GK03q24wbO9XntR93M3/TYbPLqdKcbiefbP2EUd+NYvvJ7TzT/Rk+HPihhMTKqll/oytqg67w3RQjNOamX/g8IUSpBdgDyHBkeNyXlJmEw+2o4IrOz16jOcGt/0ZYj1fxi+wB2g3ajS2kKa7MRFy5p8g+shxbUCNswfJzX4iLUdqg2BVwA2uLbtRa5wCb8veX9flRQAZwGshQSs1RSrUuZb3CLAdWwdJnoM0N0H2y2dV4LaUUL45qR7cmYTwyewvrEy7Ym1pcgp0pO/nrD3/l1fWv0rNeT+aPmM/olqOxeJgUQVQiwXVg3Dzo9yRsnQ3/uxqStphdlRBVSmRg5Hn3XfftdXy89WNO556uwIo809pduKSGT1g7rP4RKIsNn1odydg7g4zdX+AT1ha/yO5mlypEpVOqMYpKqT+BCK31OX0IlVKzgDGAr9Y6ryzOV0p9AhwBtgAu4EpgCpAH9NJa/3me95kATABo2LBh54SEhAt+NlGG0o/C//qAbzDcvQz8ZK2iCzmVmcfId1aRnuNk7qSeNAwPMLukKiHXlcv/Nv+Pj7d+TA3fGjxx5RMMaDRAuhtVRQdWwbd/g6wUGPQv6HqXdEUVogzExccRuzqWHFdO4TZfiy83t76ZnSk7+f3o7/jb/BnRfAS3trnVa3tpuB2ZKJu/x1lThagOyn15DKXUPsCutT7np4BS6nNgHBCqtU4tj/Pzj+sNLAd+1loPuFDNMplNBXM54LMbIGkT3PUT1GlrdkWVxr7jGYx6ZzW1g3359p4e1PC3m11Spbb+2HpiV8dyIO0Aw5sN55Guj1DDt4bZZYnylHkC5v4d9i41ejPc8Cb41zS7KiEqvbj4OKZtmMbRzKNEBkYytdPUwvGJO1N28sX2L/hh/w+43C76NejHbdG30Smik1fclCtoZRSiuquIoFihLYol1LEM6A0Ea62zSzpWgmIFW/IkrH4TRn0AMTeZXU2ls2bfScZ99Dvdm4Xz8e1dsVvll9vFysjL4PUNr/P1rq+JCori6e5P06OejJGtNtxuWPMm/PQchNSD0Z9C/c5mVyVElXc86zgzds5g1u5ZnM49TdvwttzW9jYGNh6I3SI3PoUwW0Wso3gEqKWU8rTIWBRw4gIh73LPL3AAsAKhpThWVJTt3xkhsevdEhIvUfdm4bw46gpW7jnBM99to7TL1gjDisQVjJg/glm7ZnFrm1uZc8McCYnVjcUCPafCHQuNmZc/HgRr3ja+FkKUm9oBtbmv030sHb2Up656iixHFo+tfIzB3w72mnGMQohLU9qg+Ef+sd2KblRK+QEdgAs13V3u+QVaAE5AZv7wFif2wrxJENXFGB8kLtlNXRpwT99mfPX7QT76db/Z5VQKKTkp/GPFP5j802SCfYKZfv10Hu32KAF2GetZbTXoBn9fCS0HweJ/woybjfGLQohy5W/z56ZWNzF/xHzevuZtmoQ04bX1rzFg9gBe/P1FDqYdNLtEIcRFKm1Q/BrQwP1nbb8bCAC+LNiglGrmYXbSizm/hlLKenYBSqkhQE9gaf5sqcJseZkwaxxY7XDTZ2Dz1GAsLsYjA1txXbtI/vXDDpZuP2Z2OV5La8338d8zfN5wliYsZVKHScwaOouY2jFmlya8gX8ojJ0O170M+36G93pBwhqzqxKiWrAoC33q9+HDQR8ye9hsBjQawDe7v2Ho3KHc9/N9rDu6TnrNCFFJlGqMIoBS6k2MmUfnAj8AbYD7gFVAf621O/+4A0AjrbW6xPNHAK8CC4B4jBbEbhhrLaYAPbXWuy9Ur4xRLGdaw9yJsGUWjJtjrG0mykR2noux769hb3IGsyZ2p12UTMRSVFJGEs/99hy/Hv6VmNoxPNv9WZqHNje7LOGtjmyEb+6A1IPQ/wno+YDRTVUIUWGOZx1n5q6ZzNo1i9TcVBnHKEQFKvfJbPLfxIrRIjgBaAycwGgpfFprnVHkuAN4DoqlPb8N8BzQCagD2IFEYBHwota6VKuTS1AsZ398CHEPGeuYXf2I2dVUOclpOYx4exVuDfMm9ySyhp/ZJZnOrd3M3DmTaRumodFM7TSVm1vdjNVyTgcEIYrLSYPv74et30LTfjDqfQiKMLsqcnKvqwAAIABJREFUIaqdbGc2C/YtYPqO6ew/vZ+IgAj+0vovjG45WmanFqKcVEhQrGwkKJajxPXGRBHN+sEtX8vd+XKy/UgaY95bTZPagcya2J0AH5vZJZkmPjWeZ1Y/w6bjm+hRrwdPd3+aqKAos8sSlYnWsOEzWPgo+NUwwmLTvmZXJUS15NZufj38K59v/5zfk4z1GIc3G86tbW+lUUgjs8sTokqRoOiBBMVyknkS/tcHlAUm/gIBYWZXVKX9vPMYd322jmva1OG9WztjtZi/NlV5K7puV52AOlxR+wqWH1pOgD2Af3T9B8OaDvOKNbpEJXVsG3xzO5zYA1f/A65+FFITYPVbRlf6vAzwCTJmcO4xBcKaml2xEFXarpRdhesxOt1O+jboy21tb6Nznc7ys16IMiBB0QMJiuXA7YIvR8OBX+FvS6BeR7MrqhY+WbWfZxdsZ0Kfpvzz+jZml1Ou4uLjiF0dS46r+HxVMbVimNZ/GrX8a5lUmahS8jLhh0dg05cQ0RZS4o2fb27HmWMs9vyJuj6HFgPMq1WIauJE9glm7pzJ17u+JjU3lTZhbbgt+jYGNR4k4xiFuAwSFD2QoHiZUuLPvcMe3hySNsKwadD5drMrrDa01jzz3TY+X5PAv0ddwS3dGppdUrkZOHsgSZlJ52yvG1iXJaOXmFCRqNJWTYOlT5d8jD0A7lklLYtCVJAcZw4L4hfwxfYvZByjEGXgcoKiDC4T59qzFN7tCRs+h7x0QBvPSRtBWSG4ntkVVitKKZ4e2parW9bmqXlbWbX3hNkllYujmUc9hsSCfUKUuVMJoC4w9tflgDVvV0w9Qgj8bH6MaTmGecPn8c4179C0RlNe3/A6A2YP4F+//YuEtATA6IEycPZAYj6LYeDsgcTFx5lcuRBVj7QoiuJS4o2Q6Mg6/zFyh90U6TkORr+7hiOns5k7qQfNI4LNLqlMHEo7xEdbP2L+vvk43U6Px0iLoigXL9bPvxl2Ab7B8Hhi+dcjhPBoV8oupu+YTlx8HE63kzbhbdh7ai957rzCY/ysfsT2iGVI0yEmViqE95EWRVF2Vr9l3EEvidxhN0Wwn52Pbu+Cr83CnZ+uIyUz78InebH41HgeX/k4Q+cNZcG+BYxuMZrHuj6Gn7X4UiB+Vj+mdppqUpWiSsvLuPAxF3OcEKJctAprxfM9n2fJ6CVMiJnAzpM7i4VEgBxXDtM2TDOpQiGqJgmKorgts4pP6OCJ2wFbvq6YekQx9UMDeP+2LhxLy2HC5+vIdbrMLumi7UzZyYPLH2TE/BH8dPAnxrUZx6IbF/HEVU/w17Z/JbZHLHUD66JQ1A2sK3eIRfnxCSrdcRY7pB8r31qEEBdUy78WUzpOwY3b4/6kzCTS8tIquCohqi7peiqKi60JlOL/CaXgmdRyL0d49v2WI0z5aiMjOtTjtbEdKsUU4puPb+aDLR/wS+IvBNmDuKX1LYxrO45Qv1CzSxPV1fcPGmOxS7w5pgANVl/ocAv0uA/Cm1VUhUIID8438RmAzWKje93uDGo8iH4N+xHiE1LB1QnhXS6n62n1XcFbeGYPBEcpulmV9k68KBdDY+px4EQm/12ymya1gph6bQuzS/JIa826Y+t4f8v7/Jb0GzV9a3Jvx3u5ufXN8stbmK/HFNg8o+SgaPeHW2bAtnmw6StY/xm0vQF63g9RnSquViFEoamdpp6zlJKvxZe7Yu4i05HJkgNLeHLVk9jWSGgU4nJIi6I4I/MEfNDfWHy6JBY7dB4PQ16pmLqER1prHvpmM3M2HGbazR0Y3iHK7JIKaa1ZdWQV7295n43JGwn3C+eOdncwpuUYAuwBZpcnxBl7lsKs24yx1xdaRzH9GPz+HvzxEeSehsa9odf90Owao5eFEKLCxMXHMW3DNI5mHiUyMJKpnaYWDlPQWrP1xFaWJCxhyYElHMk8UtjSOLDxQPo16CdLbYhqQ9ZR9ECC4kXa+QMsuA+y87uTlniHXWY99Ra5ThfjPlzLpsRUZtx9JZ0bhZlaj1u7WXZoGe9veZ/tJ7cTGRjJne3uZGTzkfjZ/C58ASHMkBJvTNC15esz68bGjIXukz3/nMtJgw2fwZp3IP0IRF5htDC2HQFW6agjhDeR0CiqOwmKHkhQLKWcNFj8OGycbvyxM/J9SDtc+jvswnSnMvMY+c4q0nOczJvckwZhFd9i53K7WJKwhPe3vM/e1L00CG7AXVfcxbCmw7Bb7RVejxAVwpkHf86CVdPgxG6o2RC63wsdbwUfaTkXwttordl2chuLDyyW0CiqDQmKHkhQLIUDq2De3+F0IvR6AK5+DGw+xr6LvcMuTLXveAYj315FnRA/vp3UgxC/iglnDreDuPg4PvzzQxLSEmhWoxl3xdzF4MaDsVmkZUVUE2437F4Eq16HQ79DQDh0mwjd7oYAc1v5hRCeSWgU1YUERQ8kKJbAkQPLXjDWTAxtDCP/Bw2vNLsqcZlW7zvBbR+tpXuzcD6+vSt2a/mtfpPrymXennl8vPVjjmQeoU1YGybETKB/w/5YlKy6I6qxhDVGYNy9yOim32m8cYOtZgOzKxNCnEdBaFxyYAmLDywuDI1X1b3KmAhHQqOoxCQoeiBB8TyStsDciZC8HbrcCQOeB1+ZwbSqmPXHIf7x7Rb+emVDXhjRrsyXzchyZDF792w+3fYpx7OPE1M7hokxE+kd1btSLNEhRIU5th1Wv2l0TdUarhgNPadCnWizKxNClKCk0Diw0UD6N+wvoVFUKhIUPZCgeBaX07jLvfwlo1vU8LdknGEV9dLCnbz3yz6eGtqWv/VqUibXzMjLYOaumXy+7XNO5Z6iW2Q3JsRMoFtkNwmIQpTkdKIx6c36T8GRCS0GGhPfNOohM6UK4eWKhsYlCUs4nHFYQqOodCQoeiBBsYiT+2Du3yFxLUSPhCGvyriZKszt1kz6cgOLtx/lg3FduLZtnUu+VmpOKl/u/JIvd3xJel46vaJ6MSFmAh0jOpZhxUJUA1kpsO4j+O09yDoB9bsaLYythoBFumsL4e08hkZl46p6nkNjSct3CFGRJCh6IEERo7vTuo9hyZPGbKVDXoV2N8pd7GogO8/F2PfXsDc5g2/+3p3oehd3x/NE9gk+3/Y5X+/6mixnFtc2vJa7Yu4iOly6zQlxWRzZsOlLo1vqqQMQ3gJ63mdMFmbzNbs6IUQpaK3ZfnK7MRGOh9DodDt5+Y+XyXHlFJ7jZ/UjtkeshEVR4SQoelDtg2JaEnw3Bfb+CM36w/C3IaSe2VWJCpSclsPwt1ehNcyf0pM6IRdex/Bo5lE+2foJ3+75FofbweDGg7nrirtoEdqiAioWohpxOWHHfPj1dTi6BYIi4ap7jLHjfiFnjkuJNyYe2zKryAzUN0GPKTIDtRBewFNoPJ+6gXVZMnpJBVYnhARFj6p1UNw6B+IeNGY3Hfg8dL1LWhGrqe1H0hjz3mqa1A5k1sTuBPjYPHaHiakdw0d/fsT8ffNBw7Bmw/jbFX+jUUgjsz+CEFWb1hC/3BhDHr8cfEOMsHjVPXD0T1nTVohKpCA03hx383mPmTlkJi3DWmK3yBrDomJIUPSgWgbF7FMQ9zBsnQ1RnWHk+1CrudlVCZP9vPMYd322jmvb1GFYz2M8tya2WHcYi7KABpvFxsgWI7mz3Z3UC5LWZyEq3JGNsGoabJ8PygraDdp1/uPtAXDPKmlZFMLLDJw9kKTMpPPu97f5c0WtK2hfuz0dIzoSUztGJsUR5UaCogfVLiju+xnmTYbMZLj6Uej1IFhlwXNh+PjX/Tz3/XZqRKzDHT77nP3+tgC+H7mAiIAIE6oTQhSTEg8zboHjO0s+zmKHzuNhyCsVU5cQolTi4uOIXR17zhjF+zvfT7hfOJuOb2Jj8kZ2pezClX8zqHnN5oXBsUNEBxoGN5RZxUWZuJygKEmissvLgqVPwx8fQK1WcMtXUE9mpBTFDWrvw5y9W9mXsRWrtqCUu9j+LEcW2w5BRCuTChRCnBHWFE6ff5xTIbcDtnwtQVEIL1MwYc35Zj0d3GQwYPzu3Xpia2FwXJKwhG/3fAtAmF9YseDYNrwtvlaZ8EpULGlRrMwS18HciXByL1w1Ga55Cuz+ZlclvIDD7WBT8iZWJq5kReIK9p3eB4DbEYwzPRprQAJWvzPdYtx5NXEffIJF9/emUXigWWULIQrE1gRK+fv5779CRLQssyFEJefWbuJT4wuD4+bjm0lISwDAbrHTNrytERxrd6B9RHtq+dcyuWJRGUjXUw+qdFB0OeCX/4OVr0BIFIx4B5r0MbsqYbIT2SdYmbiSlYdXsubIGjIcGdgsNjrX6UzGqeas314Xt08iOrcubmcIAY3fwep7HO22k5M0CjI6cUu3hjw/op3ZH0UI8WJ9yEsv/fH+YdC4JzTubTwi2sgkZkJUASezT7L5+GY2JW9i0/FNbD2xFUf+5FYNgxvSIaKD8ajdgWY1mxnzDghRhARFD6psUEzeCXMnQNJmaP8XuO4l8JMB0NWRy+1i68mtheFw+8ntAET4R9C7fm96R/XmqnpXEWgPpN0zi8nIdQJgDdqGK7sxSjmxBW/FnReOK7M1AEG+NrY+O8i0zySEyPf9g7Dh8+KznZ7NYjfWxm3WD/avhAMrIdVofSCgFjTuZTya9IFaLSU4ClEF5Lny2H5ye2Fw3Ji8kZScFACC7cHERMTQsbbRXfWKWlcQYA845xqeZj+X9R2rLgmKHlS5oOh2w+/vwo/Pgm8QDJsGbYaZXZWoYKdzT7P6yGpWJK5g1eFVnMo9hUVZaF+7Pb2jetO7fm9ahbY6ZwB8k8fiStuJjb3/ug6bVe5ICmGqlHh4tyc4ss5/jKdZT08lwIFfjdC4fyWkJRrbg+qcCY6N+0B4MwmOQlQBWmsS0xPZeHwjm5KN4LgvdR8ajVVZaRnako4RHQvHOq4/tt7jRDuxPWIlLFZREhQ9qFJBMfUQzLvH+MXf8jq44Q0IktkpqwOtNbtP7WblYWOs4ebjm3FrNzV9a9Izqid9ovrQo14PavrVLPE6RVsUL6RmgJ3+rSMYFB1Jnxa18fexlsVHEUJcrD1LL28dRa3h1H4jOBa0OKbnj00Ormt0UW3S2wiPoU0kOApRRaTlpbHl+BZjnGPyZrac2EK2MxswlsRya/c559QNrMuS0UsqulRRASQoelAlgqLWsHkGLHzUWE9r8EvQ8Vb5ZV7FZToy+S3pt8IupclZyQC0CWtD7/q96VO/D+3C22G1lD7APTnvT2auPYTTff7vd6uCXi1qEx7ow487jpGW48TPbqF3i9oMio7kmtYRhAb6XPbnE0JchJR4WPO2MbtpXgb4BEHMWOg++eLXT9QaTu4zAmNBi2Om8fOFkPr5oTE/PNZsWPr6Vr8FW2YVqe8m6DFF1ncUwks43U52n9rNxuSNvLT2pfMeN7TpUBqGNKRRcCMa1WhEo+BGBPkEVWClojxIUPSg0gfFzBOwYCrs/B4a9TQmrAltbHZVohxorUlIS2BF4gpWHl7JumPrcLqdBNoD6VGvB72jetMrqhe1A2pf8nsknMxk8OsryXacf/Fuf7u1cNZTh8vN2v0pLNl2lCXbj5F0OgerRdG1cSiDoiMZ0LYO9UPPHfcghKhEtIYTu2H/ivzuqr9C1gljX82GRhfVgvBYI+rc8y+3xVMIUeEGzh5IUmbSOdt9LD6E+4efsy/ML4xGIY1oGNzQeA5pSOOQxjQIbuBx/KPwPhIUPfD6oFjSXdjknbDgPsg5Df2fMu4cX0TrkfB+ua5c1h1dVxgOD6UfAqBZjWaFE9F0jOiI3Wovs/dctiuZSdM34HC5i7Us2iwKu9XCO7d2ol+rc7s0a6358/Bplmw7xuJtR9mTnAFAdL0QBraNZFC7OrSqEywLAwtR2WkNyTvyWxtXQMIqyD5l7Attkh8a+xhdVZ3ZlzaGUghhqrj4uBLHKOY4cziUfoiDaQdJSE8wntMSSEhL4Hj28WLXivCPMFog8wNko+BGNAppRIOQBrLmoxeRoOiBVwfF892FVTZAg3ZBnStg1PtQp61pZYpL52lGsU4RnQrHGq49upZsZza+Vl+urHtlYath/eD65VpXwslMPly5n7kbD5OZ5yTQx8bIjlHc1btJqddPjD+ewdLtRmjceCgVraFhWAAD29ZhULtIOjUMxWqR0ChEped2Q/K2M+MbD6yC3NPGPt8akJsOnDvWqZDFDp3Hw5BXKqRcIUTpXOqsp1mOLA6mG8GxaIA8mH6wcOZVAIUiMjCyMDwWDZMNghpc8Ca4zMpatiQoeuC1QbE0M9lZbHDPaqjdquLqEmXG0906hULnzzsaFRRF7yhjrGHXyK742fzMKvWyJafl8OOOZBZvO8rqfSdwuDThgT5c26YOg9rVoUezWvjZpTVciCrB7YKjfxqhcekzxk3NC/EJgn8eLv/ahBCmSs9LPxMe0xOKhcm0vLTC4yzKQr3AemdaIYt0a60XVI/FBxbLrKxlTIKiB14bFEu7Npbcha0Ucl25HE4/TGJGIofSD3Eo/RCzd88m15V7zrHBPsFMv346TUKaVMlumuk5DpbvOs7ibUdZvus4GblOAnys9G1lTIbTt1UENfxLvouYcDKTD1bGM2/jETJznQT62hjRsR53925a6hZPIUQFiK0JpV10J7ieMeaxZgPjuUaD/K8bQY36YPcvvzplsh0hTJeak1rYjfVA2oHCAHkw/SCZjszC42zKhkbj8nATqpZfLWYMnUGYXxg+VplY72JIUPTAa4Pii/UhL/3Cx/kGw+OJ5V+PKJHWmtO5pwtDYNFAmJieSHJWcmFLIUCALYAsp+fWYoViy/gtFVW6qXKdLtbsO8mS7cdYuv0Yx9NzsVkU3ZuFMzA6kgFt6hBZo3hL6qWOoRRCmKC0v8usPtBuNJw+BKkJcPrwuS2RgREegmQj43WNBsbawZdCJtsRwqtprTmZc7JYN9aPtn50wfOC7cGE+YcR5ufh4R9GuF944esavjWwqOq9NrQERQ+8NiiW9i6sUvBMarmXI4xpo49mHj0nBCamG68zHBnFjq/tX5sGwQ2oH1y/2HOD4AaE+oYy6NtBHmcUq65rFLndmo2HUlmy/ShLth1j/wnj7mH7BjUZFF2HgW0jsVvVRc3KKoQw2aX2jnE5jbUcTx+C1IPGOsGpCWden04EV17x6/iHFQmSjfKDZJFg6Vfj3PcuzTAPsyfbkdZOIc5xvllZQ31Dua/TfaTkpBiPbOP5ZM5JUnJSSM1N9bg+pEVZCPUNLRYsiwbJgnBZsN3f5l9ir6/KOH6yQoKiUsoCTAUmAo2B48As4GmtdWYJp17S+Uqp64EngfZALvAT8A+t9f7S1Ou1QVFaFMvExX6jZjmyClsECwJgQSA8knEEpz6zGL3NYqN+UP1iAbB+kPF1VHAU/raSu0ldaEax6kxrzd7kDJbkT4azJdGYGCPEz0Z6jrPEWyg2i+KWbg15fkS7iin2LN7eLdab6/Pm2ry9Pq+trbyCmNsNGceKBMn8R9Fgmb9weCHfGue2SO77GeJ/gSI/289h5jCPPUtxfz0Ot9OBjTM1OrFhsdmxjP3C9NbOw/HbOBT3H9qdWEQA2WThz9Zag2kw5BGimkZLbZW0Pm+uDeCL3/7H6zvfJk+d+YvARyvubz2ZcVdNPO95LreL03mnCwNkQYg8mX3yTLgs8ija5bUoP6vfOQGy4LEjcTOLk5biLJIjS1Ob2SoqKE4D7gPmAguBNsC9wErgWq09xPhLPF8pNQqYDWwGPgBqAPcDLqCL1vrIher12qAoYxQvm6cg5mvx5eGuD9MqrFVhACwaBk/mnCx2jRCfkGJBsGgYjAiIuKjF7M9XY2W742SGI6nZ/LjjGM9+tx1XKX4WBfpY2fTMQOzWiu1G4u3dYr25Pm+uzdvr8+baADYv+4YWyydjw4mPOtMbIE9bcWJjT9+3ad9vTNm+qdbGOsOnDxZpkTxYPFjmZVz4OgWsPnDNM8bNWd9g8A0xuroWvg4Gn2Cw2sruM6TE43q7B1ZX9nkPcVn9sU5ebVrLoin/batAbd5enzfXVrS+pYF23g4L4ajNSqTTxeSUNAZkOsq0vhxnDqdyThVrlSzaUlk0bKbkpOB0n/+mU6TDxX+bPWvqv11Jyj0oKqWigT+BuVrrG4tsvxd4A/ir1vqrsjhfKWUHDgBOIFprnZG/vQOwHvhIaz3hQjV7bVAschc2LjCAaaE1C78Rpp5KZUhmlvndYfJVZNhxuV1kO7PJcmaR5cgq9nXR52xnNh/++eF57wQVKJiauVirYHB9GgQZzzV8PXRVEqZp8lhcaafFACDAx0oNfzs1/O2E+NsJ8bMXvja22c56febri52FNeFkpld3i/Xm+ry5NvDu+ry5NjhTX23nEf5m/YFR1l8JJIdM/Jjj6sVHrus5bqtX8fVpDdmn0C83oUynDLP5Fw+P5wuVviH54TLo3G2+QWAPIO3bqfj9Ob3YH+pny9NWcmLGEXLjtLL8FKVyOH4boZ/1I0CdOylbgSzty6nxyyq8BcqbawPvrs+bawPvri9x31bs06/h2ka1jaFhZ1Fa89v+ZNP+7S7kcoJiaW+R3QIo4PWztn8AvATcCpw3KF7k+VcD9TC6pBbeFtRab1JKLQfGKqUma61LaJLzYmFN4abPiVtwF7GhQeRYjJaRJLuN2FphYPVhyLAPvSIkFm21S8pMInZ1LFprBjQeUCzAeQp12c5sjyGvcNtZxxVtHbwc71zzDvWD6xMVFCWzYlUigb42MnJL6CKWz8dmYUq/5pzOdhQ+0rIdJJ7KYvsR43VmXslT9vvYLPnB0uYxSNbID54F27747QB5zpKv6XC5+XDlflO6xX6wMh6Hq8QOHabV5821gXfX5821wZn6Duo6POO8g2ecd5xzjM2M+pSCgDByLQH4uUvoFpsvRwXg9+hOY03Ikh55HralJhR5nQYltDicqc9CsHZ7+luzGB/lwvLndAgKMlo9rfkT8FjsxV9bfc5MzlP42pZ/jI/REurpmLOvVaSgQ3H/oTYlfxYbTg7F/Zeoez+58GcuQ95cG3h3fd5cG3h3fYk//JdObgd1nS6S7OdGp0iny9R/u/JU2hbFxcC1QIDWOvesfauAllrr2mVxvlLqceBFYIDW+sezjv0X8E+gndZ6W0k1t2/fXv/www8X/GxmuWXBTSSf1R0SIMgWwLjo8WhtTA/s1u4zD9zFXp99jNYaF67C7Vpr3NpdeEyx1xS/xtnn7D61u9i4vUvla/HF3+6Pn9UPf7s//lZ//G3Gw8/mV/j12duK7it2rt2f8QvHczz7+DnvFeEfwYyhMy67ZlHx/m/RDr7bdKRY97qz2SyK4R2i+Mfg1iVey+lyk57rJD3HSXqOw3jOdpBW8DrXSUZOkdc5rjPH5Tq41Pm9LApa1gnBosBiUViVwqIUFgVWi8JiUShF4XarMrYZx4JFKZQFrBRsp/AYq1KogvPyt6v88z5ZdYC8CwQKAB+rhanXtoAi7SwFXxX8jaiK7lOejyl23FnHnL3tpYU7S13bE0PaXPC487nU1WZe+H5Hqet7cuil13cpvLk28P761n3/ER3ZhVWdv0aXtrCR1nQZeuflv6HWWNwOrM5M7M4srM4sbK4srI5M7K4zr22OTKx7F2PHjVW5sOPCihsrLixoVP6j4GuLzY7F7cRSBr+PS+JWNtwWK1rZcTly0FBYhTu/KiC/KiB/uwptDCq/YqUAhVYWUPmfQCnAglYWNGdtVxZA5W+zoBVFvlb8f3t3HiZFfedx/P3tmXEYIHFXMYiDIuiKFwaPIKJEJESTkE2IioYNLrqIrlciWTc8utFIzKO7PubYR01clSQmUYNHMMYkSjxwjS4BDxTjAUkACSQKHlFuZua7f/yqoaunZrqnB7qqnc9L++mZOqY//aO7q75dv/oVVrctR3691mW/JUf+39S29UTxouPHW72O+qHROZ5m8WWinNumFXyAhGW2feoV9HRJWM4Klwu/ty6+j7pOjhRvz1dP/WEnF0wp+hBL/EyLTyx+zskfhNunbV10F/VlZms4/LSSyyWr/Dj+1udm02Dx13nS5rjF66k//PSKH6cSLc/Npt5a+HN9A4t6NdIKtBk8sfvbNLa18eW33mHcho2s8170vWRRVbOVY+DAgTu96+li4EPu3j9h3l3ARKDR3be0W7mL65vZ9cCFwMHu/nLRsucDNwInuXu74SPN7BzgHICmpqYjP/axj5V8bml5fOXjFa+bH43JzMj/F/6PphdNaze/cL2C3wv/9jubOh5xdfCug6nL1VFn0a3o55zltv2+M64X+PqG11ny1pLY6FY5y3HAbgfQv3e7l5jUgI1bWpm/7E3aOikUczlj5ODdadqle+ePdsYdWr2Nra1OS2sbLa3Os6+9Xfb6u/dtjP5OuGhK/uM1/3v+MdrNxwuWJZoXrePR/G0/h3ki0rO0KyIT79vCvXly4Zm0bEfzC/5G4eOHn6GwVClcZvuyHc1rv25+Wjnrxss3r/iLIpHuaHNjQdMuDN7aQv/WUIC7gw39RMrJ2nvggQd2etfT3oSRR5NsKlgmsVDs4vq9o9+Tli9cth13vxm4GcIRxZtuuqmDh0zfpAcm8cbGN9pN79fUj1tPvJUcOXKWI5fLbf/ZclW7UHtH+bJy1O7hFQ8za/Es1mxcwx5NezB12FTGDRqXdizphif/uJbL7l1MS1v7gTvqczmuPmUYx+7Xr+q5xl43j/VbSn+b32eXeh69ZMzODxRpa3Na3TnxW4+zoZPz2PKaGuq497xR237fVrrG78LPHl+msC71omWSvvLNT/rCrfM7PcduW7b6On509tEll0vSnaJ5yqwFbCzRrRhCvh9OHVHx41TizAxng9rId2Drq0yvu4c6WqgvOLLY4jlaqefbrafySt3Qqud7ZNYVHM8zsUzFWjw3H/YSAAAQR0lEQVTHPI5i3NSZVUwWbJw1gaZOzhPL2+CN9J56XxUSbdd5tu2fBRu8kd5n/SxMc4/Ns8IPLy9YN7acx5eLf0LG1rOC9TbdMYVeVvrMqE3eQK/PR9cLLPoMS9zLa/c5V+r39utsvvtcGsvNdur3Si5XzJIydMGme84vq+02egNNp97Yrcfqqk33XNAum+HslXsLaIhuREcUs1d7DBw4sOJ1yy0UNwAdDa3Wq2CZHbF+/r6xwscCoKGhgebm5lKLpWbGx2ckXkLh0lGXcuDgzrvWVUNH+WaMmpGJdp3SPIUpo6akHUN2oNOamzn6kP259YllzHluFeu3tNBnl3o+d3gzZ48enNqlACYefxg/XbCyZLfY00bsk8p747QxHy4r3+dH7MNhQ6t77vPpYzaWne2YYf9QxWTB6SdsLjvfsYcdUMVk2c4GtZJvN670wR0OtrPa9mRSCvl+N+pMPvLSoyUH7Xjm4CmptN38/UdwxNr7Sw6282y/zzKyyvm6lG149bs8z18wqvx8x4yuYjKY/9yxHF5mtqNHV/+L9/mLjmV4mflGjD6xisk6y7Z9BPYtXsfKfp9maAb2kXekcseYXw30M7Ok4q0ZWNtRt9MK1l9dMD1pWYBVZWTOtPFDxnPlqCsZ0GcAhjGgz4BMXWcv6/nk/WnQ7n24asKhvDjzJJZdM54XZ57EVRMOTfV6cdNGDyl5OY6Guhxnjx5cpURxWc6X5WyQ7XxZzga1ky8/2M6wzbMYsvl2hm2exddazuI1759avlPGjebituls8Ea2eLwr/RavY4M3cnHbdE4ZV91CIm/v8f9OS4njCC3Us/f4S6qUaLssZ4Ns58tyNsh2vixn29nKLRQXRsvG+meYWS9gOFDqOhRdWX9hdH9Mwt8ZCbwLLCkzd6aNHzKeuafO5YUpLzD31LmZK8Kynk+kGgbt3ofvTj6CpoY66nPxTkH1OaOpoY7vTj4itWI2y/mynC3r+bKcTfm6n23S5KlMaLuW2W1jec+baHPjPW9idttYJrRdy6TJU1Nru+Yhh7B0zI2dFrJLx9yYymUAspwt6/mynC3r+bKcbWcrdzCbYcDzdHwdxDPc/SfRtP2ABnd/pcL1G4AVwFbi11H8MPAs8AN3P7tU5sxeR1FEatKKN9dnrltsreTLcras58tyNuV7/2aDcF27lb+8jkPW/npbt93f9/ske4+/JPUd4ixny3q+LGfLer4sZ+tMd66jWFahGD1IfjTSOcCvgIOALwJPAmPdwxCUZrYcGOTuVsn60bITgdmE4vIW4IPAdMLZuke6e8mupyoURURERESkJ+tOoVjuYDYAFwPLCZefGA+sBa4Hrigs8nbE+u5+t5ltBL4KXEcYAfURYEY5RaKIiIiIiIhUruwjirVGRxRFRERERKQn684RxXIHsxEREREREZEeQoWiiIiIiIiIxKhQFBERERERkRgViiIiIiIiIhKjQlFERERERERiVCiKiIiIiIhIjApFERERERERiVGhKCIiIiIiIjEqFEVERERERCRGhaKIiIiIiIjEqFAUERERERGRGBWKIiIiIiIiEqNCUURERERERGJUKIqIiIiIiEiMCkURERERERGJUaEoIiIiIiIiMSoURUREREREJEaFooiIiIiIiMSoUBQREREREZEYFYoiIiIiIiISo0JRREREREREYlQoioiIiIiISIwKRREREREREYkxd087w05hZmuAFWnnKFM/YG3aIWqU2q5yarvKqe0qp7arnNque9R+lVPbVU5tVzm1XeUK226Qu+9RyR953xaKtcTMnnb3o9LOUYvUdpVT21VObVc5tV3l1Hbdo/arnNqucmq7yqntKrej2k5dT0VERERERCRGhaKIiIiIiIjEqFDMhpvTDlDD1HaVU9tVTm1XObVd5dR23aP2q5zarnJqu8qp7Sq3Q9pO5yiKiIiIiIhIjI4oioiIiIiISIwKRREREREREYlRoSgiIiIiIiIxKhRTYmY5M5tuZq+Y2SYzW2lm3zSzPmlnyzIzO8DMvm5m881sjZm9Z2aLzOw/1HZdY2a9zWyZmbmZ3ZB2nlpgZruZ2XVm9ofofbvGzB4zs9FpZ8syM+trZpeZ2eLoPbvWzJ4yszPNzNLOlwVmdqmZ3W1mf4rek8tLLH+0mT0ctee7ZvagmQ2vUtxMKbftzKyXmU0zs5+b2XIz2xitc6eZHVTl2JnQ1ddd0brXRuus24kRM6uStjOzM8zsyeg9u87MXjSzy6sQN1Mq+Lz7pJk9YmZ/NbP1ZvZqtC3uX6XImdHV/WAzG2pm95nZ21HbPWFmY8t+PA1mkw4z+2/gi8Ac4NfAQcBFwBPAOHdvSzFeZpnZfwIXAPcD84GtwAnAacALwEh335hewtphZtcB5wJ9gRvd/cKUI2WamQ0C5hHaaxawBNgVOAx4yN1/ml667DKzHPA4MAq4jfC+7Q1MAkYA17r7jPQSZoOZOfAW8CxwJPCuu+/bwbIjCa/FVUD+S54LgQ8Bo9x98c7OmyXltp2ZHQi8DPwWmAusBoYA5wF9gE+4+2NVip0JXXndFa03HFgIbCLsS/bdmTmzqKttZ2bfB6YA9xLev63AYKCfu5+9s/NmSRc/76YRRvB8BrgdWA98BDgLeA0Y5u7rqxA7E7qyH2xm+wELgBbgO8DfgGnAocAn3f3hkg/o7rpV+QYcArQB9xZNvwhw4J/SzpjVG3AUsGvC9G9EbXdh2hlr4QYcEX1wfDlqtxvSzpT1G+FLnJXAgLSz1NINOCZ6jX27aPouwJ+Ad9LOmIUbMKTg5xeB5Z0suwB4F2gumNYcTZub9nPJatsBuwPDE6YfDGwGnk77uWS17YrWqSMUifcTCp51aT+PrLcdMDX6HDwj7dxZuHWx7V4lfKnTq2h6fr9vQtrPp8ptV/Z+MHAX4QuJ4QXT+gIrona1Uo+nrqfpmAQYobovdAuwAZhc9UQ1wt2fdve/JcyaHd0fWs08tcjM6givtQeBn6UcpyaY2UeB4whHv/5iZg1m1jvtXDXig9H96sKJ7r4FWEv4drjHc/c/lbOcme1P+Db9bndfVbD+KuBuYJyZ7blzUmZTuW3n7m+6+6KE6S8RdlZ73Paj3LYr8kVCcX3RDo5TU7rwnjXgUuBZd/9xNO0DPbnbfRdfdx8E3nb3TUXT89uUHrUNKXc/OOqG+hlgXuHnnruvA24FDiBsSzqlQjEdHyEcUVxQODF6EyyijH84aWdgdP96qilqw3TgQEJXNSnPp6L718zsF8BGYL2ZLTEzfbHTuQXAO8BXzGyime0TnTNxDaHL0ZWppqs9+e3D/yXMm0/4EvLI6sWpfVH36AFo+1FS1AX/KmCmu69IO0+NGArsBzxlZpeb2ZuEo//vmNlNZtbjuu120UPAwRbG8TjIzPY2s5OBywmnNTyabrzMKN4PPgxopONtBZRRb9R3P5dUYC9grbtvTpi3ChhlZrtE37hLCdERsisIXSnvSDlOppnZYGAm8HV3X25m+6abqGYMje5vAZYSzjNpJHTd/bGZNbj7D9IKl2Xu/raZfYbwDeZdBbPeA05x9/vSSVaz9oruVyXMy09rrlKW94vzCIXiVWkHqQHfA5YB30o7SA3Jbz9OJ3S5/wahDT9NGCdgqJmN9ahfoLTzJcJ57V8ibHPzfgCc6+6tqaTKkA72g3fItkKFYjp6E86HSLKpYBkViuX5DjASuMzdX007TMZpI1+ZD0T37wEn5L/EMbM5hPPsrjaz21yDUHVkHaFr3/3AU8BuhJPx7zCzz7r7b9IMV2PyXZ6TtiGbipaREsxsFPBNwiAQV6ccJ9PMbBLwCeA4d29JO08NyW8/9gA+7tsHELk36n46hdCuv04jXA3YShi0Zg7wC8IpWicB/0I4/25aetEyI2k/eIdsK1QopmMDYXS6JL0KlpESzOwqQhfKm939mrTzZFnURfJE4KPuvjXtPDUmP5LunYVH+qOjZfcD/0z41vjlNMJlmZkNIxSH0939poLpdxKKx1vMbD99K1y2/LahMWGeth9dYGZHAr8knOv0qYRzoCRiZrsRdkZnuftTaeepMfntxypvP8rkbYRCcQwqFNuJuoU/SKhXji046npP1IV3hpnNTmjXHqOT/eAdsq3QOYrpWA30M7Okf7xmQrdUHU0swcyuBL5K6H7wr+mmybbotfYt4FfAX81s/2hQjEHRIrtG0/4utZDZ9ufo/q8J8/4S3f99lbLUmumEjdLdhRPdfQNhJ30QsG/1Y9Ws/AAOSV2G8tOSuhpJATM7AvgNYbj4EwoHBpJEXyNcQuSW/PYj2oY0EcZr2d/M9k43YmZp+1G544DRhKsEFHfNzW9Tjq9upOwosR+8Q7YVKhTTsZDQ9iMKJ5pZL2A48HQaoWqJmX2NsOH6EXC2+vaX1ETo9jKecI5d/jYvmj85+r1HXcupC/IDTw1MmJef9kaVstSa/AapLmFefdG9lLYwuj8mYd5IwvDoz1QvTu0xs8MJRWK+K7kGZSltEKFQ/B3xbcgIQve1peiIWEcWE44qJu2wa/vROW0/OlDGfvBiQrfTjrYVUEa9oUIxHbMJG/OLi6ZPI3zg3l71RDXEzK4gjJT4Y+AsnRdWlvXAxITb+dH8B6Pf708lXfbdR9ipnFw4Qp2ZDQAmAEvd/Q9phcu4l6L7MwsnRkevPwu8DfyxyplqVvQ6exqYaGb5wQqIfp4IPOruSUcuhG1F4sOEz8QT3H1ZypFqxX+RvA15iXC+00RC7wEpEvWe+Bmwp5l9rmj2edH9r6qbqmbktx9fMLOGonlnRvcL6WHK2Q+OLoPxC2CMmX24YN2+hIMCSym6+kLiY+lATDrM7HpCn+I5hA+IgwjXJnoSGKviJ5mZXQDcQDix+XLCZUYKva6BMcoXjXq6DLjR3XW5jE6Y2TnA/wC/B75PGL0uP1rip919borxMisaTv9ZQteq2wmfcbsRvhjbF7jA3b+bWsCMMLMz2N4V/CLC6+ub0e8r8tdfi5YdBTxG6NJ2fcE6/Qnn8TxfldAZUW7bRa/FZwivv5kkf0Exx917zHXZuvK662D9ecBR7t7jLvHQxffsPoSd8l0J79nlhMsujQd+5O5TqhQ7E7rYdvcApxAGnPoJ2wez+UfCZR6O60nnuHdlPzjqHr6AMCDQtwmXZZkGDAPGu/tDJR/Q3XVL4UY4jP5vwKuEQ8OrCOeQ9U07W5ZvwA8JR2M7us1LO2Mt3Qg76g7ckHaWWrgBJxM2TOsJRxjnEnbMU8+W5RvhGmK3EQqbrdHG6n+Bk9POlpUboRt42Z9rhO5EjxBGlH2PcK2xI9J+HlluO8KAIZ1tPxzYN+3nk8W2K7H+urSfRy20XbS9vR1YQxjV/mXgEiCX9nPJctsRisivAM8TuvBuBpYQRinuk/ZzSaHturQfTDgQ9XPC9Yw3AL8FxpX7eDqiKCIiIiIiIjE6R1FERERERERiVCiKiIiIiIhIjApFERERERERiVGhKCIiIiIiIjEqFEVERERERCRGhaKIiIiIiIjEqFAUERERERGRGBWKIiIiIiIiEqNCUURERERERGL+HwRzTKWkhidFAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1080x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats\n",
    "import matplotlib.pyplot as plt\n",
    "plt.figure(figsize=(15,8))\n",
    "\n",
    "# PDF LAM = 1\n",
    "plt.scatter(np.arange(20),stats.poisson.pmf(np.arange(20), mu=1),s=100)\n",
    "plt.plot(np.arange(20),stats.poisson.pmf(np.arange(20), mu=1))\n",
    "\n",
    "# PDF LAM = 5\n",
    "plt.scatter(np.arange(20),stats.poisson.pmf(np.arange(20), mu=5),s=100)\n",
    "plt.plot(np.arange(20),stats.poisson.pmf(np.arange(20), mu=5))\n",
    "\n",
    "# PDF LAM = 10\n",
    "plt.scatter(np.arange(20),stats.poisson.pmf(np.arange(20), mu=10))\n",
    "plt.plot(np.arange(20),stats.poisson.pmf(np.arange(20), mu=10))\n",
    "\n",
    "# LEGEND\n",
    "plt.text(x=3, y=.1, s=\"$\\lambda = 1$\", alpha=.75, rotation=-65, weight=\"bold\", color=\"#008fd5\")\n",
    "plt.text(x=8.25, y=.075, s=\"$\\lambda = 5$\", alpha=.75, rotation=-35, weight=\"bold\", color=\"#fc4f30\")\n",
    "plt.text(x=14.5, y=.06, s=\"$\\lambda = 10$\", alpha=.75, rotation=-20, weight=\"bold\", color=\"#e5ae38\")\n",
    "\n",
    "# TICKS\n",
    "plt.xticks(range(21)[::2])\n",
    "plt.tick_params(axis = 'both', which = 'major', labelsize = 18)\n",
    "plt.axhline(y = 0, color = 'black', linewidth = 1.3, alpha = .7)\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
